diff --git a/.travis.yml b/.travis.yml
index 5a8e2be9..e8789873 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,4 +1,5 @@
 sudo: false
+dist: trusty
 language: cpp
 compiler:
 - gcc
@@ -9,10 +10,11 @@ addons:
     - ubuntu-toolchain-r-test
     packages:
     - g++-5
+    - clang
 
 install:
 - export CXX="g++-5"
-- script/configure
+- scan-build script/configure
 
 script:
 - script/ci
diff --git a/script/ci b/script/ci
index 70035525..64690944 100755
--- a/script/ci
+++ b/script/ci
@@ -2,6 +2,9 @@
 
 set -e
 
+. script/lib.sh
+
 script/fetch-fixtures
 script/check-mallocs
-script/test
+scan_build make
+script/test -b
diff --git a/script/lib.sh b/script/lib.sh
new file mode 100755
index 00000000..786fc51d
--- /dev/null
+++ b/script/lib.sh
@@ -0,0 +1,26 @@
+#!/usr/bin/env bash
+
+function scan_build {
+  extra_args=()
+
+  # AFAICT, in the trusty travis container the scan-build tool is from the 3.4
+  # installation. Therefore, by default it will use clang-3.4 when analysing code
+  # which doesn't support the '-std=c++14' (it is available via '-std=c++1y').
+  # Use the system-wide installed clang instead which is 3.5 and does support
+  # '-std=c++14'.
+  extra_args+=("--use-analyzer=$(which clang)")
+
+  # scan-build will try to guess which CXX should be used to compile the actual
+  # code, which is usually g++ but we need g++5 in the CI. Explicitly pass
+  # $CC/$CXX to scan-build if they are set in the environment.
+
+  if [[ ! -z "$CC" ]]; then
+    extra_args+=("--use-cc=$CC")
+  fi
+
+  if [[ ! -z "$CXX" ]]; then
+    extra_args+=("--use-c++=$CXX")
+  fi
+
+  scan-build "${extra_args[@]}" --status-bugs "$@"
+}
diff --git a/script/test b/script/test
index 39f21793..35c7ec33 100755
--- a/script/test
+++ b/script/test
@@ -2,6 +2,8 @@
 
 set -e
 
+. script/lib.sh
+
 function usage {
   cat <<-EOF
 USAGE
@@ -12,6 +14,8 @@ OPTIONS
 
   -h  print this message
 
+  -b  run make under scan-build static analyzer
+
   -d  run tests in a debugger (either lldb or gdb)
 
   -g  run tests with valgrind's memcheck tool
@@ -26,6 +30,7 @@ OPTIONS
 
   -z  pipe tests' stderr to \`dot(1)\` to render an SVG log
 
+
 EOF
 }
 
@@ -37,8 +42,9 @@ args=()
 target=tests
 export BUILDTYPE=Test
 cmd="out/${BUILDTYPE}/${target}"
+run_scan_build=
 
-while getopts "df:s:gGhpvS" option; do
+while getopts "bdf:s:gGhpvS" option; do
   case ${option} in
     h)
       usage
@@ -69,6 +75,9 @@ while getopts "df:s:gGhpvS" option; do
     S)
       mode=SVG
       ;;
+    b)
+      run_scan_build=true
+      ;;
   esac
 done
 
@@ -78,7 +87,11 @@ else
   args+=("--reporter=singleline")
 fi
 
-make $target
+if [[ ! -z "$run_scan_build" ]]; then
+	scan_build make $target
+else
+	make $target
+fi
 args=${args:-""}
 
 if [[ -n $profile ]]; then