In this study, we consider the anisotropic or direction-dependent ignition of single crystal pentaerythritol tetranitrate (PETN). Previous experiments have shown that the anisotropic ignition of PETN is induced by the crystal orientation and micro-structural features at the molecular scale. Numerical models have taken the standard approach of considering only the isotropic ignition via ignition and the growth process, which assume a perfect isotropy or orientation independence for the ignition of an explosive crystal. Based on our previously announced anisotropic concept, which depends on strain and the strain rate, we developed an adaptive mesh refinement technique to carry out three-dimensional simulations of the anisotropic ignition of a PETN crystal subjected to directional shock loadings.