In spite of extremely simple concept of the classical CA, they have generally speaking a complex enough dynamics. In very many cases theoretical research of their dynamics collides with essential enough difficulties. For this reason, computer simulation of these structures that in the empirical way allows to research their dynamics is a rather powerful tool. For this reason this question is quite natural for considering within the present paper, considering the fact that CA at the formal level represent the dynamical systems of highly parallel substitutions. The detailed enough discussion of the problem of computer simulation of the CA is presented.