The development of armour materials and systems is a very expensive business, especially when it involves lengthy ballistic trials. Penetration and perforation events are also highly complex and involve competition between alternative failure mechanisms. The physical conditions within an impact zone also vary, with location, in temperature, strain-rate, strain, stress state and pressure. Numerical modelling and computer simulations help understand these complexities and add value to the design process. This chapter describes some of the underpinning principles by covering the range of computer codes available, the types of processors used, and the breadth of both yield strength models and damage criteria which are employed to describe how an armour material flows, fractures and fails. At the end of the chapter, four worked examples illustrate the choices available when modelling armour/anti-armour interactions. The annexures provide excellent sources of data for the various material models and failure criteria. © 2017, Elsevier.