A modern theory of underground structures design has been developed in Russia. The basic principle in the theory is that of joint contact interaction of rock mass and a lining as elements of “rock-support” system subjected to external loads. Main postulate of the theory is that the elastic medium can be taken as the rock mass model. All underground structures design methods of the theory are based on rigorous analytical solutions of the corresponding elasticity theory contact problems. The analytical design method for vertical shaft lining is based on this theory. In generally the reason of shaft lining loading is intact rock mass stress state induced by rock own weight and tectonic forces. Consequently the magnitudes and directions of in situ principal stresses in the rock mass are the important input data. Shaft sinking technology plays an important role in shaft lining loading.