The paper is devoted to the stability analysis of the body force action models, used in the lattice Boltzmann method. The six widely used models are investigated. Only single-phase fluids are considered. Stability investigation is based on the application of the von Neumann method to the linear approximation of the system of the nonlinear lattice Boltzmann equations. An analysis is realized by the construction of the stability domains in the parameter space. The integral characteristics in dependence on the relaxation time are investigated. The rotation of the body force vector to the flow direction on some angle is considered. It is demonstrated, that the force provides a stabilizing effect if it acts in the opposite direction to the velocity vector. As the main result of the analysis of the stability domains, it is demonstrated, that the better stability properties take place for the implicit model. In the class of the explicit models, the exact difference method is preferable.