The study of physical mechanisms of rock materials destruction allows obtaining the information necessary for the development of new technologies for mining and processing of minerals. Furthermore, such knowledge makes it possible to assess in real-life conditions the influence of external factors, for example, water, on the strength characteristics of mine workings and constructions, including the underground ones. The authors study the deformation behavior and special aspects of the destruction of small-sized specimens cut from the model viscoelastic materials - rock materials (carbonaceous quartzite, serpentinite, and artificial sandstone) under the diametrical compression - indirect stretching. Laboratory studies and subsequent modeling of the structure and properties of rock materials performed on small-sized specimens make it possible to solve the task not attracting the expensive test equipment and without violating the integrity of the specimens. During the study, small-sized specimens in the form of cylinders were produced from model viscoelastic materials. The mechanical properties of carbonaceous quartzite, serpentinite, and artificial sandstone specimens were estimated in the initial state and after a 24-hour water soak test. The study showed the influence of water on the change of a type of the specimens’ deformation behavior. The authors mapped the specimens’ side surfaces and created the topograms of the working surfaces before and after the tests. Based on them, the metallographic analysis of the geometric characteristics of cracks was performed at the macro- and microscopic levels. It was suggested that the change of a type of deformation behavior of rock materials, as well as the decrease in the strength properties of test rock materials specimens under the influence of water, are explained by the Rehbinder effect mechanisms.