Modern milking machines need some additional studies to meet the requirements as to milking equipment. An imperfect design of a teatcup results in an incomplete milking of cows. The availability of devices for milk flow stimulation promotes an increase in a cow milk yielding capacity. But here arises a problem of an un-controlled axial motion of a teatcup on a teat. As a result, a full milkflow is reduced, particularly at the final stages of milking. There is an effect of an increase in an inner diameter of a liner barrel, which causes that teatcups fall down. A scientific problem of the mitigation of some negative developments with the view to improve the efficiency of a teatcup arises. In a teatcup shell a liner is in a detended position during milking and resting periods. Thus, it under constant stretching. It results in a loss of elasticity irrespective of the material, as well as in reduction ofthe period of service maintenance. The use of a device for supporting a liner which is in a stretched state only during the milkflow, will result in an increase of a teatcup efficiency. The suggested automatic pneumatic mechanism releases a liner from the load during the resting period. The dependence of a tension force of a liner from the surface area of an annular membrane has been established. It has been proven that the membrane surface of 0.00065 m2 provides tension for a mechanism performance irrespective of operating vacuum pressure. The regression equation which connects geometrical parameters of an operating system with the efforts directed at the opening of a leading membrane has been received. A suitability of operation of using a pneumatic tightening device has been substantiated. An insignificant axial motion of a liner during a cycle of milking creates a stimulating effect. As a result, a completeness of miliking increases by 3-8%.