Since the exact analytical solutions for rapid solidification process are available only for special boundary conditions, numerical techniques have to be applied for more general boundary conditions. In this paper we will describe a finite difference method for simulation of rapid solidification that is based on control volume methodology and interface-tracking technique. Heat transfer computer study will be realized for solidification with and without melt undercooling at the interface. Such numerical method will be applied for thermal history analysis of solidifying nickel on copper substrate.