The solidification models basing on the Fourier equation with the additional term controlling the kinetics of phase transition are discussed. The different approaches to this term definition lead to the different solidification models, in particular the macro and the macro/micro ones can be taken into account. In the case of macro description the equation in which the parameter called a substitute thermal capacity is considered, while in the case of macro/micro approach the linear or exponential models of crystallization can be introduced. The solution of the problem can be found using the numerical methods. In this paper the boundary element method using discretization in time is applied, the examples of numerical simulations are also shown.