Requirements to critical elements of transport and logistics systems have been increased due urbanization in the territories of Russia and the world. Bridge bearings, which perceive the vertical and horizontal loads from the bridge span, as well as absorb thermal expansion and contraction, shrinkage, seismic disturbances, etc. refer to such elements. Requirements to strength, durability, wear resistance, operation maintenance-free periods, etc., imposed on the bridge bearing are increasing due to a stable growth of loads on the bridge elements and increase in vehicle fleets. Recently, international and Russian companies have been engaged in development of new polymeric and composite materials, which have improved physical and mechanical, frictional, thermo-mechanical and rheological properties and can be used as a thin layer of sliding bearings bridges. A number of problems are outlined in studying material properties and geometric configuration of bridge bearings in order to rationalize the work of its structure. Three topical problems of solid mechanics are reviewed in the work. This is the identification of qualitative and quantitative patterns of the deformation behavior of modern antifriction polymer and composite materials as relatively thin sliding layers of bridge spherical bearings in order to formulate scientifically grounded recommendations for the selection of the interlayer material regarding the study unit operation. This is an analysis of the influence of the sliding layer material physical and mechanical, frictional, thermomechanical and rheological properties on the structure deformation as a whole and the change in the contact zone parameters, in particular. It is an analysis of the influence of the sliding layer geometric configuration on the structure performance. A significant decrease in the area of full adhesions of the contact surfaces, including up to 0, and the occurrence or increase in the area of the divergence of the contact surfaces (no contact) is observed during frictional contact taking into account the lubrication on the mating surfaces. The surface percentage on which the contact surfaces divergence (no contact) is observed decreases, on average by more than 2 times, if the sliding layer thickness is increased.