This paper is concerned with the estimation of axisymmetric stresses induced in an imperfectly bonded thick orthotropic buried pipeline due to seismic excitation (p-wave) travelling in the surrounding medium. The shell has been assumed to be imperfectly bonded to the surrounding medium. Particular attention has been focused on the analysis of the effect of stiffness and damping of the surrounding ground on the axial and hoop stresses. A thick shell theory formulation has been used and only axisymmetric behaviour of the shell has been investigated. The relative influence of the variation of orthotropic parameters on the stresses in the shell has also been studied for different angles of incidence of the p- wave. Results have been obtained for different soil conditions - hard (rocky), medium hard and soft. It is observed that both the stiffness and damping parameters in axial as well as radial direction reduce the axial stresses of the shell, significantly. On the other hand, the stiffness and damping parameters in radial direction reduce the hoop stresses of the shell significantly, while those in the axial direction give no variation in the hoop stresses.