Formation of stationary current filaments is studied in a planar layered structure of gas discharge coupled to a high-Ohmic semiconductor and driven by a stationary voltage (the gas discharge-semiconductor system, GDSS). The simulations are carried out in 2D. The model is based on the diffusion-drift theory of gas discharges. Multiple steady-state solutions in GDSS are found for the first time. The computed discharge parameters are found to be in reasonable agreement with the experiment. Results support the evidence that the thermal mechanism is responsible for the instability in GDSS, under considered conditions. This is also supported by the linear stability analysis of the homogeneous stationary state: with heating of the gas excluded, the instability does not form a spatial structure, it is homogeneous and purely growing without oscillations. Including the gas heating into the model changes the dispersion relation drastically. Published by AIP Publishing.