diff --git a/stan/math/prim/err/check_finite.hpp b/stan/math/prim/err/check_finite.hpp
index 2e92cd2ca80..d3c95f12115 100644
--- a/stan/math/prim/err/check_finite.hpp
+++ b/stan/math/prim/err/check_finite.hpp
@@ -15,11 +15,25 @@
 namespace stan {
 namespace math {
 namespace internal {
+/**
+ * Return true if y is finite
+ *
+ * @tparam T_y type of y
+ * @param y parameter to check
+ * @return boolean
+ */
 template <typename T_y>
 bool is_finite(const T_y& y) {
   return is_scal_finite(y);
 }
 
+/**
+ * Return true if every element of the matrix y is finite
+ *
+ * @tparam T_y type of elements y
+ * @param y matrix to check
+ * @return boolean
+ */
 template <typename T_y, int R, int C>
 bool is_finite(const Eigen::Matrix<T_y, R, C>& y) {
   bool all = true;
@@ -29,6 +43,13 @@ bool is_finite(const Eigen::Matrix<T_y, R, C>& y) {
   return all;
 }
 
+/**
+ * Return true if every element of the vector y is finite
+ *
+ * @tparam T_y type of elements y
+ * @param y vector to check
+ * @return boolean
+ */
 template <typename T_y>
 bool is_finite(const std::vector<T_y>& y) {
   bool all = true;
diff --git a/test/unit/math/prim/err/check_finite_test.cpp b/test/unit/math/prim/err/check_finite_test.cpp
index 5416ea3d04e..b439bf99ebc 100644
--- a/test/unit/math/prim/err/check_finite_test.cpp
+++ b/test/unit/math/prim/err/check_finite_test.cpp
@@ -24,6 +24,30 @@ TEST(ErrorHandlingArr, CheckFinite_Vector) {
       << "check_finite should throw exception on NaN";
 }
 
+TEST(ErrorHandlingArr, CheckFinite_std_vector_std_vector) {
+  using stan::math::check_finite;
+  const char* function = "check_finite";
+  std::vector<double> x = {-1, 0, 1};
+  std::vector<std::vector<double>> xx = {x};
+  ASSERT_NO_THROW(check_finite(function, "x", xx))
+      << "check_finite should be true with finite x";
+
+  x = {-1, 0, std::numeric_limits<double>::infinity()};
+  xx = {x};
+  EXPECT_THROW(check_finite(function, "x", xx), std::domain_error)
+      << "check_finite should throw exception on Inf";
+
+  x = {-1, 0, -std::numeric_limits<double>::infinity()};
+  xx = {x};
+  EXPECT_THROW(check_finite(function, "x", xx), std::domain_error)
+      << "check_finite should throw exception on -Inf";
+
+  x = {-1, 0, std::numeric_limits<double>::quiet_NaN()};
+  xx = {x};
+  EXPECT_THROW(check_finite(function, "x", xx), std::domain_error)
+      << "check_finite should throw exception on NaN";
+}
+
 TEST(ErrorHandlingArr, CheckFinite_nan) {
   using stan::math::check_finite;
   const char* function = "check_finite";
@@ -94,26 +118,20 @@ TEST(ErrorHandlingMat, CheckFinite_std_vector_Matrix) {
 
   x.resize(3);
   x << -1, 0, std::numeric_limits<double>::infinity();
-
-  std::vector<Eigen::Matrix<double, Eigen::Dynamic, 1>> xvi = {x};
-
-  EXPECT_THROW(check_finite(function, "x", xvi), std::domain_error)
+  xv = {x};
+  EXPECT_THROW(check_finite(function, "x", xv), std::domain_error)
       << "check_finite should throw exception on Inf";
 
   x.resize(3);
   x << -1, 0, -std::numeric_limits<double>::infinity();
-
-  std::vector<Eigen::Matrix<double, Eigen::Dynamic, 1>> nxvi = {x};
-
-  EXPECT_THROW(check_finite(function, "x", nxvi), std::domain_error)
+  xv = {x};
+  EXPECT_THROW(check_finite(function, "x", xv), std::domain_error)
       << "check_finite should throw exception on -Inf";
 
   x.resize(3);
   x << -1, 0, std::numeric_limits<double>::quiet_NaN();
-
-  std::vector<Eigen::Matrix<double, Eigen::Dynamic, 1>> xvn = {x};
-
-  EXPECT_THROW(check_finite(function, "x", xvn), std::domain_error)
+  xv = {x};
+  EXPECT_THROW(check_finite(function, "x", xv), std::domain_error)
       << "check_finite should throw exception on NaN";
 }