Fundamental understanding of dynamic behavior of polycrystalline ceramics is advanced through constitutive theory development and computational modeling. At the mesoscale, microstructures of silicon carbide grains (hexagonal crystal structure) or aluminum oxynitride grains (cubic crystal structure) are subjected to compression or shear at high rates with varying confining pressure. Each grain is resolved by numerous three-dimensional finite elements, and behavior of each grain is modeled using nonlinear anisotropic elasticity. Cohesive fracture models and post-fracture contact are included. Normal and Weibull failure statistics from many simulations are collected and analyzed. Results demonstrate effects of load directionality, confinement, dilatation, elastic anisotropy and elastic nonlinearity, and grain boundary fracture properties on macroscopic (average) failure stresses for loading conditions in the ballistic regime. Predictions demonstrate reasonable agreement with data from macroscopic plate impact, unconfined compression, and flexure experiments.