The behaviour of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling is studied. In strong coupling limit, the Mott–Hubbard phase state is presented; the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k + \pi$ are coupled via the effective $\lambda$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occurred at a critical value of the one-site Hubbard repulsion $U_{C}$ ($U_{C}$ = 3.904 and $U_{C}$ = 5.125 are calculated values for hexagonal and triangular lattices, respectively). Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The pro-posed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.