diff --git a/src/stan/optimization/lbfgs_update.hpp b/src/stan/optimization/lbfgs_update.hpp
index ba9d7afcb62..1f8719d4b12 100644
--- a/src/stan/optimization/lbfgs_update.hpp
+++ b/src/stan/optimization/lbfgs_update.hpp
@@ -2,7 +2,7 @@
 #define STAN_OPTIMIZATION_LBFGS_UPDATE_HPP
 
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <boost/circular_buffer.hpp>
+#include <stan/util/ring_buffer.hpp>
 #include <tuple>
 #include <vector>
 
@@ -72,8 +72,8 @@ class LBFGSUpdate {
    **/
   inline void search_direction(VectorT &pk, const VectorT &gk) const {
     std::vector<Scalar> alphas(_buf.size());
-    typename boost::circular_buffer<UpdateT>::const_reverse_iterator buf_rit;
-    typename boost::circular_buffer<UpdateT>::const_iterator buf_it;
+    typename stan::util::ring_buffer<UpdateT>::const_reverse_iterator buf_rit;
+    typename stan::util::ring_buffer<UpdateT>::const_iterator buf_it;
     typename std::vector<Scalar>::const_iterator alpha_it;
     typename std::vector<Scalar>::reverse_iterator alpha_rit;
 
@@ -103,7 +103,7 @@ class LBFGSUpdate {
   }
 
  protected:
-  boost::circular_buffer<UpdateT> _buf;
+  stan::util::ring_buffer<UpdateT> _buf;
   Scalar _gammak;
 };
 }  // namespace optimization
diff --git a/src/stan/services/pathfinder/single.hpp b/src/stan/services/pathfinder/single.hpp
index 7202fa6dcf2..a0df4efd0f0 100644
--- a/src/stan/services/pathfinder/single.hpp
+++ b/src/stan/services/pathfinder/single.hpp
@@ -12,7 +12,7 @@
 #include <stan/services/util/initialize.hpp>
 #include <stan/services/util/create_rng.hpp>
 #include <stan/services/util/duration_diff.hpp>
-#include <boost/circular_buffer.hpp>
+#include <stan/util/ring_buffer.hpp>
 #include <tbb/parallel_for.h>
 #include <tbb/concurrent_queue.h>
 #include <tbb/task_group.h>
@@ -659,8 +659,8 @@ inline auto pathfinder_lbfgs_single(
                 + std::to_string(lbfgs.logp()));
   }
   int ret = 0;
-  boost::circular_buffer<Eigen::VectorXd> param_buff(max_history_size);
-  boost::circular_buffer<Eigen::VectorXd> grad_buff(max_history_size);
+  stan::util::ring_buffer<Eigen::VectorXd> param_buff(max_history_size);
+  stan::util::ring_buffer<Eigen::VectorXd> grad_buff(max_history_size);
   Eigen::VectorXd prev_params
       = Eigen::Map<Eigen::VectorXd>(cont_vector.data(), cont_vector.size());
   std::size_t history_size = 0;
diff --git a/src/stan/util/ring_buffer.hpp b/src/stan/util/ring_buffer.hpp
new file mode 100644
index 00000000000..caf65a85830
--- /dev/null
+++ b/src/stan/util/ring_buffer.hpp
@@ -0,0 +1,130 @@
+#ifndef STAN_UTIL_RING_BUFFER_HPP
+#define STAN_UTIL_RING_BUFFER_HPP
+
+#include <algorithm>
+#include <cstddef>
+#include <iterator>
+#include <stdexcept>
+#include <utility>
+#include <vector>
+
+namespace stan {
+namespace util {
+
+/** Fixed-capacity buffer that overwrites its oldest element when full. */
+template <typename T>
+class ring_buffer {
+ public:
+  explicit ring_buffer(size_t capacity) : buf_(capacity) {
+    if (capacity == 0) {
+      throw std::domain_error("ring_buffer capacity must be > 0");
+    }
+  }
+
+  size_t size() const { return size_; }
+  size_t capacity() const { return buf_.size(); }
+
+  void clear() {
+    start_ = 0;
+    size_ = 0;
+  }
+
+  void push_back() {
+    if (size_ < capacity()) {
+      ++size_;
+    } else {
+      start_ = (start_ + 1) % capacity();
+    }
+  }
+
+  template <typename U>
+  void push_back(U&& value) {
+    push_back();
+    back() = std::forward<U>(value);
+  }
+
+  T& back() { return (*this)[size_ - 1]; }
+
+  T& operator[](size_t i) { return buf_[(start_ + i) % capacity()]; }
+  const T& operator[](size_t i) const {
+    return buf_[(start_ + i) % capacity()];
+  }
+
+  void rset_capacity(size_t new_capacity) {
+    if (new_capacity == 0) {
+      throw std::domain_error("ring_buffer capacity must be > 0");
+    }
+    if (new_capacity == capacity()) {
+      return;
+    }
+
+    std::vector<T> new_buf(new_capacity);
+    size_t keep = std::min(size_, new_capacity);
+    for (size_t i = 0; i < keep; ++i) {
+      new_buf[i] = std::move((*this)[size_ - keep + i]);
+    }
+    buf_ = std::move(new_buf);
+    start_ = 0;
+    size_ = keep;
+  }
+
+  class const_iterator {
+   public:
+    using iterator_category = std::bidirectional_iterator_tag;
+    using value_type = T;
+    using difference_type = std::ptrdiff_t;
+    using pointer = const T*;
+    using reference = const T&;
+
+    const_iterator() = default;
+    const_iterator(const ring_buffer* buffer, size_t pos)
+        : buffer_(buffer), pos_(pos) {}
+
+    reference operator*() const { return (*buffer_)[pos_]; }
+
+    const_iterator& operator++() {
+      ++pos_;
+      return *this;
+    }
+    const_iterator operator++(int) {
+      const_iterator result = *this;
+      ++*this;
+      return result;
+    }
+    const_iterator& operator--() {
+      --pos_;
+      return *this;
+    }
+
+    bool operator==(const const_iterator& other) const {
+      return buffer_ == other.buffer_ && pos_ == other.pos_;
+    }
+    bool operator!=(const const_iterator& other) const {
+      return !(*this == other);
+    }
+
+   private:
+    const ring_buffer* buffer_ = nullptr;
+    size_t pos_ = 0;
+  };
+
+  const_iterator begin() const { return const_iterator(this, 0); }
+  const_iterator end() const { return const_iterator(this, size_); }
+
+  using const_reverse_iterator = std::reverse_iterator<const_iterator>;
+  const_reverse_iterator rbegin() const {
+    return const_reverse_iterator(end());
+  }
+  const_reverse_iterator rend() const {
+    return const_reverse_iterator(begin());
+  }
+
+ private:
+  std::vector<T> buf_;
+  size_t start_ = 0;
+  size_t size_ = 0;
+};
+
+}  // namespace util
+}  // namespace stan
+#endif
diff --git a/src/stan/variational/advi.hpp b/src/stan/variational/advi.hpp
index 681ce65e82c..579e222b41d 100644
--- a/src/stan/variational/advi.hpp
+++ b/src/stan/variational/advi.hpp
@@ -9,7 +9,7 @@
 #include <stan/variational/print_progress.hpp>
 #include <stan/variational/families/normal_fullrank.hpp>
 #include <stan/variational/families/normal_meanfield.hpp>
-#include <boost/circular_buffer.hpp>
+#include <stan/util/ring_buffer.hpp>
 #include <algorithm>
 #include <chrono>
 #include <limits>
@@ -335,7 +335,7 @@ class advi {
     // Heuristic to estimate how far to look back in rolling window
     int cb_size
         = static_cast<int>(std::max(0.1 * max_iterations / eval_elbo_, 2.0));
-    boost::circular_buffer<double> elbo_diff(cb_size);
+    stan::util::ring_buffer<double> elbo_diff(cb_size);
 
     logger.info("Begin stochastic gradient ascent.");
     logger.info(
@@ -528,10 +528,10 @@ class advi {
    * @param[in] cb circular buffer with some number of values in it.
    * @return median of values in circular buffer.
    */
-  double circ_buff_median(const boost::circular_buffer<double>& cb) const {
+  double circ_buff_median(const stan::util::ring_buffer<double>& cb) const {
     // FIXME: naive implementation; creates a copy as a vector
     std::vector<double> v;
-    for (boost::circular_buffer<double>::const_iterator i = cb.begin();
+    for (stan::util::ring_buffer<double>::const_iterator i = cb.begin();
          i != cb.end(); ++i) {
       v.push_back(*i);
     }