A model of the structure of the low-temperature orthorhombic phase (O') of LaMnO3 was constructed using pair potentials with explicitly allowing for the many-body Jahn-Teller contribution to the crystal energy. Microscopic factors that cause structural instability of the LaMnO3 lattice against rotations of oxygen octahedra and Jahn-Teller distortions were studied. Elastic and dielectric constants of the crystal in the O' phase and in phases distorted by the Jahn-Teller effect, as well as the frequencies of fundamental vibration modes, were calculated.