Abstract: In practical engineering, when the surrounding rock and the lining contact with each other, the interface between the lining and the surrounding rock mass is not fully smooth, nor can it bear arbitrarily large friction. The tangential sliding will occur on the contact surface between the lining and the surrounding rock when the shear stress on the interface is greater than the maximum static friction. The state of the minimum relative sliding on the interface is considered as the true working state of the lining, and this kind of contact is called frictional slip contact. Coulomb friction model is used to simulate frictional slip contact between the lining and the surrounding rock mass. Under the premise of considering the mechanical process of the support delay, the equations of stress boundary condition, stress continuous condition and displacement continuous condition are listed by the plane elastic complex variable method. Combined with the optimization theory, a general frictional slip contact solution method is established. Furthermore, in the process of solving the optimization problem by the mixed penalty function method, the optimization model is greatly simplified by reducing the number of design variables, the iteration speed of the optimization process and the precision of the optimization results are improved. On this basis, the stress analytic solutions for a lined hydraulic circular tunnel under the interaction of the lining and the surrounding rock are derived. This method can simultaneously solve the two limiting contact cases of pure bond contact and pure slip contact and has generality. At the same time, the threshold of friction coefficient satisfying the pure bond contact under different conditions are obtained by using a precise calculation method. At last, the variation laws of tangential stresses on the boundaries of the lining and the surrounding rock are obtained.