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The subject of the research is a sub-rail foundation containing a viscous element. The purpose of the study is to evaluate the effect of including a viscous element in the elastic system (rails, sleepers, ballast, etc.) on the overall rigidity of a railway track. The design of a sub-rail foundation with a viscous element is described by the generalized Maxwell model and contains a shell filled with a Newtonian fluid, in particular air. Pneumatic shells with different thicknesses were considered. The modeling was carried out in the finite element analysis environment. Mathematical models of a track section with a sub-rail device containing a pneumatic shell were constructed. The calculation results showed the absence of a sharp increase in internal force factors and stress concentration in typical track sections when laying a sub-rail foundation with a pneumatic element. A change in the overall rigidity in the vertical plane did not lead to a significant change in bending stresses in the edges of the rails. With a small shell thickness, the bending stresses in the upper area of the sleeper decrease to 35 %, and in the lower area by 15 %. The maximum increase of up to 8 % is observed with a sharp difference in the shell thicknesses. Compressive stresses on the sleeper in the under-rail zone increase with a small shell thickness of the device due to the redistribution of forces to a smaller number of under-rail supports when the overall rigidity of the structure changes. Increasing the shell thickness to 40 cm leads to an increase in mechanical stresses of up to 20 %, which is an acceptable value with a large margin. The use of under-rail foundations with a viscous element is recommended for temporary railway tracks when laying them instead of ballast and sleepers, which allows for the track to be quickly laid and also quickly dismantled.