For computer simulation of the mechanical behavior of materials and various media, methods of continuum mechanics are mainly used. Continuum approach uses highly developed mathematical apparatus of continuous functions, and capabilities of this approach are extremely wide and well known. However, for a number of very important processes, such as severe plastic deformation, mass mixing, damage initiation and development, material fragmentation, and so on, continuum methods of solid mechanics face certain hard difficulties. As a result, a great interest for the approach based on a discrete description of materials and media has been growing up in recent years. It is obvious that both continuum and discrete approaches have their own advantages and disadvantages. A great number of commercial software has been created for solving numerous scientific and engineering problems based on continuum mechanics. Hence, the main line of discrete approach development seems to be not a substitute but a supplement to continuum methods in solving complex specific problems based on a coupling of the continuum and discrete approaches. This chapter shows how to solve this problem on the example of the finitedifference method for numerical solution of dynamic problems on elasticplastic deformation of continua, which is based on the continuum approach, and the movable cellular automaton method based on the discrete approach. Two particular applications of the coupled method are considered. The first example concerns simulation of target penetration by long rod at the macroscale. The second one deals with simulation of sliding friction at the scale of contact patch (mesoscale).
