The use of finite-difference and finite-element computer codes to solve problems involving fast, transient loading is commonplace. A large number of commercial codes exist and are applied to problems ranging from fairly low to extremely high damage levels (e.g., design of containment structures to mitigate effects of industrial accidents; protection of buildings and people from blast and impact loading; foreign object impact damage; and design of space structures to withstand impacts of small particles moving at hypervelocity, a case where the pressures generated exceed material strength by an order of magnitude). But, what happens if code predictions do not correspond with reality? This paper discusses various factors related to the computational mesh that can lead to disagreement between computations and experience. Subsequent papers focus on problems associated with contact surfaces and material transport algorithms, constitutive models, and the use of material data at strain rates appropriate to the problem. It is limited to problems involving fast, transient loading, which can be addressed by commercial finite-difference and finite-element computer codes.