Car tire is made of a composite material, whose individual components have significantly different mechanical properties. Its primary task is to transfer forces generated by the vehicles drive system so that the driver maintains sufficient control over the vehicle, as well as to preserve optimal performance characteristics. Presence of snow and slush, especially on roads with significant inclination leads to a drastic deterioration of the vehicles traction. In this case, in order to ensure sufficient control over the vehicle snow chains are used, whose task is to change the nature of the interaction between the tire and the surface through an increase in the radial forces operating in the area of contact, by increasing the surface area, and the expansion of the wheels outer surface macrostructure. Stress distribution in the tire, especially in the area of direct contact between the tire, the chain and the surface is a result of the mechanical properties of tires composite constituents, chain geometrical characteristics, tire pressure, hardness, and surface type, thickness and density of the snow cover, and temperature of the system. Value of these stresses has a direct and significant impact on the issue of safety, operating characteristics of the vehicle, and the durability of road surface and tires. In order to evaluate the stresses in the tire equipped with chains, authors' previous numerical model was further developed, which has been earlier successfully used to estimate the value of the deflection, and the surface area of the contact area as a function of load. Model takes into account all relevant geometric and material features of actual tire-chain-surface as well as the loads acting on the wheel. In this paper numerical model of the tire equipped with snow chains, and the results of the stress distribution obtained by numerical simulation for pressure and load conditions corresponding to a typical real were presented.