The paper presents a generalized mathematical model describing the dynamics of magnetic field influence on a peristaltic flow of a conducting liquid in a two dimensional channel. A method using the stream function (/spl Psi/), vorticity (/spl xi/) and magnetic potential (A) is used. The Galerkin method is applied to obtain a system of three variational identities. A numerical finite element algorithm based on the second order elements is developed. The algorithm uses the Newton-Raphson method to solve the resulting nonlinear system. A simulator based on the formulated algorithm is constructed using object-oriented technology.