The paper presents the results of numerical simulation of plasma equilibrium and stability in the MEPHIST-0 tokamak with SIEMNED software and comparison of simulation results with experiment. The determined characteristics of the vacuum chamber shows that it significantly affects the entire discharge. For various scenarios of the inductor operation, a comparison of experimental data and simulated currents and magnetic fields induced in the chamber was carried out. For the steady state tokamak operation, a numerical study of equilibrium plasma configurations was carried out depending on the currents in the poloidal magnetic field coils and plasma current. The vertical plasma instability is investigated. The limiting values of plasma ellipticity preventing the vertical plasma instability was numerically determined. Numerical simulations show that plasma equilibrium is supported by induced currents. It was shown numerically that magnetic configuration with "zero of higher order" have been obtained before plasma shot, suggesting consistence between the simulation results and observation..