  The cell motility problem has been investigated for a long time. Today, many
biologists, physicists, and mathematicians are looking for new research
instruments for this process. A simple 2D model of a free-boundary cell moving
on a homogeneous isotropic surface is presented in the paper. It describes the
dynamics of the complex actomyosin liquid, whose special properties influence
the boundary dynamics and cell motility. The model consists of a system of
equations with the free boundary domain and contains a non-local term. In this
work, we present a numerical solution of this problem.
