The structure and dynamics of the crystal lattice of MeF2 fluorites (Me = Ca, Sr, Ba, and Pb) under external hydrostatic compression (0-3.5 GPa) are calculated within the shell model in the pair potential approximation. The first-order structural phase transition from the cubic to the orthorhombic phase in these crystals under pressure is investigated. The effect of chemical pressure on the BaF2 crystal is analyzed by the simulation of mixed crystals, namely, Ba1 - xCaxF2 and Ba1 - xSrxF2. It is demonstrated that the supercell method, as applied to the simulation of mixed crystals, results in a lower lattice energy per formula unit as compared to the lattice energy obtained by the virtual-crystal method. (C) 2002 MAIK "Nauka / Interperiodica".