This paper investigates the possibility to reduce the compressibility of lattice Boltzmann fluid models by introducing a repulsive force between nearest neighbor lattice Boltzmann particles. This new interaction is based on the Shan–Chen model. The interest of this approach is that it implements the physical mechanism responsible for the incompressibility of real fluids and retains the natural interpretation of the fluid density and fluid momentum. The new state equation shows that the compressibility factor decreases as the repulsive interaction increases. However, numerical instabilities limit the value of the acceptable repulsion. We investigate several situations, such as the Poiseuille flow with pressure gradient, a static fluid subject to gravity and the Womersley flow to evaluate the benefits of our approach. Globally, the compressibility of lattice Boltzmann fluids can be reduced by a factor of 4.