The formation of a non-equilibrium steady-state distribution function of particles with the power law interaction potentials $U\,{=}\,\alpha/r^{\rm s}$, where $1 \,{\le}\, \beta \,{<}\, 4$, is studied numerically. Consideration is based on the one-dimensional nonlinear kinetic equation of a Landau–Fokker–Planck type in the presence of particle (energy) sources. Non-equilibrium quasi steady-state local distributions exist inside the momentum interval between the energy (particle) source and the bulk (or sink) of the particle distribution and have the form of gradually decreasing functions. Numerical calculations based on the completely conservative difference schemes are accompanied by the analytical consideration and comparison with the experimental results is given. Obtained results can be useful in connection with the development of high-power particle and energy sources and for the prediction of the semiconductors behavior with an intrinsic or extrinsic conductivity under the action of particle fluxes or electromagnetic radiation.