A cellular model for a computer simulation of dendrite growth in alloys is described. In this model temperature and concentration at the interphase boundary are not prescribed as boundary conditions but their evolution is calculated with the use of transport equations and a kinetic equation which relates the local solidification rate in each cell containing the interface with thermo-chemical conditions and an interface curvature averaged through the cell. The simulation was carried out for Al-Si alloys. The dependence of the growth velocity and tip radius on the supercooling are computed and compared with analytical model data.