The main purpose of the study is to investigate the mechanical properties around an underground gas storage cavern in bedded salt rock. Firstly, considering the characteristics of the salt rock formation in China, the mechanical model was simplified into a hollow cylinder, which containing non-salt interlayer. In terms of elastic theory, Love displacement function was developed, and the elastic general solution of stress and deformation components were obtained after determining the undetermined coefficients. Under the same condition, numerical simulation was carried out. The validity of the elastic general solution is verified by comparing to numerical simulation results. Furthermore, Based on the feasible general elastic solution, viscoelastic solution was obtained through Laplace transformation and inverse Laplace transform, which could provide reference for the study on the stability and tightness of underground gas storage carven during operation to some extent.