Using a mathematical model of competitive crystallization of polymorphic metals a numerical analysis of formation kinetics of the metastable polytype of lanthanum (µ-La), which is fixed in the products of quenching from the liquid state in a mixture with crystallization of the equilibrium f.c.c. βmodification, is carried out. The interval of rapidly quenched foils thicknesses is determined, within which the metastable µ-phase is formed in quantities sufficient for experimental detection. The calculated data agree with the results of X-ray phase analysis at the physically correct value of the free parameter of the model DG µβ = 5 J/mol, which has the meaning of the degree of metastability of µ-La.