A continuum model is developed for describing deformation and failure mechanisms in crystalline solids (ceramics and minerals) with the cubic spinel structure. The constitutive model describes the response under conditions pertinent to impact loading: high pressures, high strain rates, and, possibly, high temperatures. Nonlinear elasticity, anisotropy, thermoelastic coupling, dislocation glide, twinning, shear-induced fracture, and pressure-induced pore collapse are addressed. The model is applied to enable an improved understanding of transparent ceramic aluminum oxynitride (AlON). Calculations demonstrate an accurate depiction of hydrostatic and shear stresses observed experimentally in shock-loaded polycrystalline AlON. Various choices of initial resistances to slip, twinning, or shear fracture that result in similar predictions for average stresses in polycrystals but different predictions for defect densities (accumulated dislocations and twin volume fractions) are investigated. Predictions for single crystals provide insight into grain orientation effects not available from previous experimental investigations.