This paper presents a theory of elasticity solution of the axisymmetric steady-state dynamic response of a buried pipeline excited by a plane longitudinal wave (P-wave) traveling in the surrounding soil. Both the pipeline and the ground have been assumed to be linearly elastic, homogeneous and isotropic. Linear elasticity equations of motion have been solved simultaneously for the pipeline and the surrounding soil. A perfect bond between the pipeline and the ground has been assumed. The midplane deformations of the pipeline have been plotted against the nondimensional wave number of the incident wave, for different soil condition and angle of incidence of the wave. The results of the present work have been compared with those found by using a shell theory which includes the effect of shear deformation and rotary inertia. It has been found that excellent agreement exists between the results obtained by the two approaches. The present work concludes that the use of shell model, including effects of shear deformation and rotary inertia, is justified for the analysis of dynamic response of buried pipelines excited by seismic waves traveling in the ground.