© 2014 I. V. Zhukova, E. P. Kolpak and Yu. E. Balykina. The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.