diff --git a/make/cpplint b/make/cpplint
index faefee164e0..79b977478ea 100644
--- a/make/cpplint
+++ b/make/cpplint
@@ -2,4 +2,4 @@ PYTHON ?= python
 
 .PHONY: cpplint
 cpplint:
-	@$(PYTHON) $(CPPLINT)/cpplint.py --output=vs7 --counting=detailed --root=src --extension=hpp,cpp --filter=-runtime/indentation_namespace,-build/c++11,-readability/namespace,-legal/copyright,-whitespace/indent,-runtime/reference,-build/header_guard,-build/include_order,-build/include_what_you_use,-runtime/string,-build/namespaces $(shell find src/stan -name '*.hpp' -o -name '*.cpp')
+	@$(PYTHON) $(CPPLINT)/cpplint.py --output=vs7 --counting=detailed --root=src --extension=hpp,cpp --filter=-runtime/indentation_namespace,-build/c++11,-readability/namespace,-legal/copyright,-whitespace/indent,-runtime/reference,-build/header_guard,-build/include_order,-build/include_what_you_use,-runtime/string,-build/namespaces $(call findfiles,src/stan,*.hpp) $(call findfiles,src/stan,*.cpp)
diff --git a/make/libstanc b/make/libstanc
index d48bc5bc7f0..735eaf26a7d 100644
--- a/make/libstanc
+++ b/make/libstanc
@@ -1,7 +1,7 @@
 ################################################################################
 # libstanc build rules
 
-STANC_TEMPLATE_INSTANTIATION_CPP := $(shell find src/stan/lang -type f -name '*_inst.cpp') $(shell find src/stan/lang -type f -name '*_def.cpp')
+STANC_TEMPLATE_INSTANTIATION_CPP := $(call findfiles,src/stan/lang,*_inst.cpp) $(call findfiles,src/stan/lang,*_def.cpp)
 STANC_TEMPLATE_INSTANTIATION := $(STANC_TEMPLATE_INSTANTIATION_CPP:src/%.cpp=test/%.o)
 
 test/libstanc.a : $(STANC_TEMPLATE_INSTANTIATION)
diff --git a/make/tests b/make/tests
index aea7a43cbf1..80fc8728e0e 100644
--- a/make/tests
+++ b/make/tests
@@ -50,7 +50,7 @@ endif
 # needed by subset of unit tests that test stan compiler
 # all these tests are under stan/test/unit/lang
 ##
-STANC_TESTS_HEADERS := $(shell find src/test/unit/lang -type f -name '*_test.cpp')
+STANC_TESTS_HEADERS := $(call findfiles,src/test/unit/lang,*_test.cpp)
 STANC_TESTS_O := $(patsubst src/%.cpp,%.o,$(STANC_TESTS_HEADERS))
 STANC_TESTS := $(patsubst src/%.cpp,%$(EXE),$(STANC_TESTS_HEADERS))
 
@@ -64,7 +64,7 @@ $(STANC_TESTS) : LDLIBS += $(LDLIBS_STANC)
 # Target to verify header files within Stan has
 # enough include calls
 ##
-HEADER_TESTS := $(addsuffix -test,$(shell find src/stan -name '*.hpp' -type f))
+HEADER_TESTS := $(addsuffix -test,$(call findfiles,src/stan,*.hpp))
 
 ifeq ($(OS),Windows_NT)
   DEV_NULL = nul
@@ -160,7 +160,7 @@ test/test-models/stanc$(EXE) : %$(EXE) : %.o
 	@mkdir -p $(dir $@)
 	$(LINK.cpp) $< $(LDLIBS) $(OUTPUT_OPTION)
 
-TEST_MODELS = $(shell find src/test/test-models -type f -name '*.stan')
+TEST_MODELS = $(call findfiles,src/test/test-models,*.stan)
 $(patsubst src/%.stan,%.hpp,$(TEST_MODELS)) : test/test-models/%.hpp : src/test/test-models/%.stan test/test-models/stanc$(EXE)
 	@mkdir -p $(dir $@)
 	$(WINE) test/test-models/stanc$(EXE) $< --o=$@
@@ -168,7 +168,7 @@ $(patsubst src/%.stan,%.hpp,$(TEST_MODELS)) : test/test-models/%.hpp : src/test/
 ##
 # Generate C++ from Stan standalone functions
 ##
-TEST_FUNCTIONS = $(shell find src/test/test-models -type f -name '*.stanfuncs')
+TEST_FUNCTIONS = $(call findfiles,src/test/test-models,*.stanfuncs)
 $(patsubst src/%.stanfuncs,%.hpp,$(TEST_FUNCTIONS)) : test/test-models/%.hpp : src/test/test-models/%.stanfuncs test/test-models/stanc$(EXE)
 	@mkdir -p $(dir $@)
 	$(WINE) test/test-models/stanc$(EXE) $< --o=$@
@@ -193,7 +193,7 @@ test/unit/lang/stanc_helper_test.o: change-file-permissions
 # Add additional dependencies for tests that should translate Stan to hpp, but
 # isn't included in the source using `#include`.
 ##
-test/unit/lang/parser_generator_test$(EXE): $(patsubst src/%.stan,%.hpp,$(shell find src/test/test-models/good/parser-generator -type f -name '*.stan'))
+test/unit/lang/parser_generator_test$(EXE): $(patsubst src/%.stan,%.hpp,$(call findfiles,src/test/test-models/good/parser-generator,*.stan))
 
 ##
 # Compile models depends on every model within
@@ -201,10 +201,10 @@ test/unit/lang/parser_generator_test$(EXE): $(patsubst src/%.stan,%.hpp,$(shell
 # be code-generated to a *.hpp, then passed through
 # the compiler using the -fsyntax-only flag
 ##
-test/integration/compile_models_test$(EXE): $(patsubst src/%.stan,%.hpp-test,$(shell find src/test/test-models/good -type f -name '*.stan'))
+test/integration/compile_models_test$(EXE): $(patsubst src/%.stan,%.hpp-test,$(call findfiles,src/test/test-models/good,*.stan))
 
 ##
 # Same trick as above for models, but for standalone functions, using
 # "src/test/test-models/good-standalone-functions/*.stanfuncs"
 ##
-test/integration/compile_standalone_functions_test$(EXE): $(patsubst src/%.stanfuncs,%.hpp-test,$(shell find src/test/test-models/good-standalone-functions -type f -name '*.stanfuncs'))
+test/integration/compile_standalone_functions_test$(EXE): $(patsubst src/%.stanfuncs,%.hpp-test,$(call findfiles,src/test/test-models/good-standalone-functions,*.stanfuncs))
diff --git a/makefile b/makefile
index da551f3baaa..839c6595c13 100644
--- a/makefile
+++ b/makefile
@@ -108,10 +108,10 @@ help:
 ##
 # Clean up.
 ##
-MODEL_SPECS := $(shell find src/test -type f -name '*.stan')
+MODEL_SPECS := $(call findfiles,src/test,*.stan)
 .PHONY: clean clean-demo clean-dox clean-models clean-all clean-deps
 clean:
-	$(RM) $(shell find src -type f -name '*.dSYM') $(shell find src -type f -name '*.d.*')
+	$(RM) $(call findfiles,src,*.dSYM) $(call findfiles,src,*.d.*)
 	$(RM) $(wildcard $(MODEL_SPECS:%.stan=%.hpp))
 	$(RM) $(wildcard $(MODEL_SPECS:%.stan=%$(EXE)))
 	$(RM) $(wildcard $(MODEL_SPECS:%.stan=%.o))
@@ -122,12 +122,12 @@ clean-dox:
 
 clean-deps:
 	@echo '  removing dependency files'
-	$(shell find . -type f -name '*.d' -exec rm {} +)
+	$(RM) $(call findfiles,.,*.d)
 
 clean-all: clean clean-dox clean-deps clean-libraries
 	$(RM) -r test bin
 	@echo '  removing .o files'
-	$(shell find src -type f -name '*.o' -exec rm {} +)
+	$(RM) $(call findfiles,src,*.o)
 
 ##
 # Submodule related tasks