An algorithm was developed for the simulation of a phase transition in the solid state which makes it possible to obtain kinetic curves of transformation under different initial conditions (the number and arrangement of new phase nuclei, the distance between the nearest embryos). The simulation results were analyzed using the Kolmogorov-Johnson-Mehl-Avrami equation and the logistic function for determining the corresponding coefficients. The correlation between the simulation results and the experimental kinetics of the isothermal transformation of austenite in alloyed steels were shown.