Based on the Biot＇s dynamic theory,the expressions of displacements,stresses and pore pressures in saturated soil,and those of displacements and stresses on cylindrical lining in transient elastic wave condition are obtained by using the method of Laplace transform and wave function expansion.Employing the inner boundary stress free condition of the lining and the continuity conditions between the soil and the lining,the unknown coefficients in the expressions are determined.With the inverse Laplace transform,the numerical solution of the problem is presented.The wave pattern properties of dynamic stress concentration factor on the lining and influence of different shear modulus of material and thickness of lining on the dynamic stress concention factor are studied.The results show that the wave type demonstrates damping with the increase of the order n.The value of dynamic stress concentration factor is lower with the increase of the lining thickness and larger when the shear modulus of the lining is larger than that of the soil.