An anisotropic elastoviscoplasticity constitutive model for beta-cyclotetramethylene tetranitramine (beta-HMX) and alpha-cyclotrimethylene trinitramine single crystals (alpha-RDX) is developed to analyze the thermomechanical responses under shock loading. The model considers nonlinear, pressure and temperature dependent elasticity, and dislocation-based plasticity which incorporate regenerative multiplication and heterogeneous nucleation mechanisms. The proposed model is calibrated against experimental wave profiles of (011), (010), (100), ((1) over bar 11), (01 (1) over bar) orientations of HMX single crystals and (210), (100), (11 (1) over bar), (2 (1) over bar0) and (111) orientations of RDX single crystals. The model can well capture elastoplastic double wave structure, stress relaxation after the Hugoniot elastic limit as well as the arrival of plastic wave. Moreover, pressure, accumulated shear strain, and temperature contours of both HMX and RDX show obvious anisotropy and non-uniform spatial distribution, which is explained by analyzing dislocation activity with corresponding resolved shear stress on slip systems. Results provide insights into understanding ignition mechanisms and predicting ignition sensitivity of explosive single crystals as well as polymer bonded explosives at the mesoscale.