The stability of the ideal two-dimensional triangular crystal lattice, which is a single atomic layer in the FCC and HCP structures was studied. Morse and Lennard-Jones potentials were used as the interaction law. An important distinction of Morse potential from Lennard-Jones potential is that during the compression of the material to the point the interaction force remains finite. The form and number of the regions depend on the selection of the interaction potential. As parameter decreases, the intermediate region disappears. The particle dynamics method was used to verify the obtained results. If a sudden growth of the kinetic energy is observed, the deformed configuration is considered unstable. The results of analytical calculations are proved by the molecular-dynamic simulation.