The anisotropic shock sensitivity in a single crystal δ-cyclotetramethylene tetranitramine (δ-HMX) was investigated using the compress-shear reactive dynamics (CS-RD) computational protocol. Significant anisotropies in the thermo-mechanical and chemical responses were found by measuring the shear stress, energy, temperature, and chemical reactions during the dynamical process for the shock directions perpendicular to the (100), (010), (001), (110), (101), (011), and (111) planes. We predict that δ-HMX is sensitive for the shocks perpendicular to the (111), (011), (110), and (101) planes, which is intermediate to the (100) and (010) plane and is insensitive to the (001) plane. The internal energy accumulated within the duration of the surmounting shear stress barrier is a useful criterion to distinguish the sensitive directions from the less sensitive ones. The molecular origin of the anisotropic sensitivity is suggested to be the intermolecular steric arrangements across a slip plane induced by shock compression. The shear deformation induced by the shock along the sensitive direction encounters strong intermolecular contacts and has small intermolecular free space for geometry relaxation when the molecules collide, leading to high shear stress barriers and energy accumulation, which benefits the temperature increase and initial chemical bond breaking that trigger further reactions.