A two-dimensional model of the crystalline (granular) medium is considered that represents a square lattice consisting of elastically interacting spherical particles, which possess three translational and three rotational degrees of freedom. The nonlinear differential equations have been derived that describe propagation and interaction of the waves of various types in such a medium. Analytical dependences of the coefficients of these equations on the microstructure parameters have been found. When only the motion of the particles in the lattice plane is considered, the rotational degree of freedom of particles can be neglected in the field of low frequencies, and the obtained equations degenerate into the two-mode system. It is shown that in a one-dimensional case, the latest model with account of the longitudinal static deformation allows a solitonic solution on shift deformation.