Physics-based particle rebound models are essential for the accurate tracking of particles in aero engines. Current models are often informed by analysis of spherical particle impact, but particles ingested in engines typically feature edges and corners. Understanding the effects of particle shape on rebound behavior is critical for ascertaining the range of validity of existing models and for developing improved models. Here, we report on first-principle simulations of cubical particles impacting Ti-6Al-4V targets. Our simulations reveal that, in the case of normal impact at a given incident speed, the coefficient of restitution (CoR) of cubes exhibits significant scattering. The scattering and median of computed CoR show good agreement with recent experiments using sand particles of the same volume-based size, sphericity, and incident speed. Comparison with spheres impacting the same target shows that the median CoR of cubes is significantly lower than that of spheres. Further, the rebound of cubes features significant rotation and transverse velocity, which can account for ∼60% of a rebounding cube’s energy but are negligible modes of energy transfer in impacts involving spheres. We identify that the moment arm length, a parameter that characterizes the mass distribution of angular particles impacting a target, plays a key role in particle rebound, and its distribution is strongly correlated with rebound stochasticity. These findings can benefit the development of physics-based low-order models of angular particle rebound.