The anisotropic shock sensitivity in single crystal α-cyclotetramethylene tetranitramine (α-HMX) was investigated using the compress-shear reactive dynamics (CS-RD) computational protocol. Anisotropy in thermo-mechanical and chemical responses is found by measuring shear stress, energy, temperature, and chemical reactions during the dynamical process for shock directions perpendicular to the (010), (001), (100), (110), (011), (111), and (101) planes. We suggest that the internal energy accumulated within the duration of the surmounting shear stress barrier can be used as a useful criterion to distinguish the anisotropic sensitivity among various shock orientations. Accordingly, the α-HMX single crystal is predicted to be sensitive for the shock normal to the (010) plane, is intermediate to the (001) plane, and is insensitive to the (100), (110), (011), (111), and (101) planes. The molecular origin of the anisotropic sensitivity is considered to be the different intermolecular steric arrangements on the two sides of the slip plane induced by shock compression along various orientations. The shear deformation induced by shock compression along sensitive directions encounters strong intermolecular contact and has little intermolecular free space for geometry relaxation when molecules collide, leading to a high shear stress barrier and energy accumulation, which benefit a temperature increase and initial chemical bond dissociation that trigger further reactions. This validation of CS-RD indicates that this approach would be valuable in examining the anisotropic sensitivity of new energetic crystals and in evaluating which one would be least sensitive.