This dissertation concerns the analytical and numerical modeling of compressible shock in granular systems and its applications. Kinetic theory and classical thermodynamic arguments suggest that granular flows with low agitation (granular temperature) may be characterized as supersonic, experiencing almost discontinuous changes in flow properties across shock fronts created by obstructing bodies. Uniform and non-uniform flows are studied analytically and with discrete element numerical simulations in different geometries. We derive a set of algebraic relations to describe property changes local to the shock and expand the analysis with use of a system of coupled shock depth-averaged differential equations. These expressions are applied to uniform flow incident on straight wedge obstructions and comparison with simulations reveals good quantitative agreement. Finally we make use of discrete element simulations and apply kinetic theory analysis to shear flow about circular bodies to explain the production of propeller-shaped density features about embedded moons in the rings of Saturn. These density features are interpreted as being predominantly created by collisional processes, in contrast to prior studies where gravitation is incorporated. We adapt the general depth- averaged differential equations for application to this system and find reasonable qualitative predictions for the shock front.