Impulsive stimulated thermal scattering (ISTS) was used to determine the complete set of second-order elastic constants for pentaerythritol tetranitrate (PETN) and cyclotrimethylene trinitramine (RDX) single crystals. Despite the weak scattering efficiency of these materials, excellent signal quality was obtained by using an optical heterodyne detection approach. The elastic constants for PETN agree well with previous values obtained from ultrasonic velocity measurements. The elastic constants for RDX are consistent with previous values obtained from ultrasonic velocity measurements and from resonant ultrasound spectroscopy, but show significant differences with values obtained from Brillouin scattering data. The present results demonstrate that the ISTS method, with optical heterodyne detection, provides a useful and accurate approach for determining the elastic constants of energetic crystals.