Oil and gas pipelines that go through an active normal fault often deform largely and cause serious disasters. On the basis of the beam theory of the elastic foundation and assuming a shape function for the deformed pipeline, a new analytical method is proposed to calculate the pipeline strain under a normal fault. The length of the deformed pipeline is calculated by using a simplified structural mechanical model. Moreover, a three-dimensional solid finite element model (3D FEM) is developed to calculate the pipeline strain under different working conditions. The developed analytical solution and the numerical results of 3D FEM are compared with the results of the two traditional methods (the dissipated energy method and the Karamitros method). The strain development law predicted by the proposed method and the 3D FEM is in good agreement with that of the dissipated energy method and the Karamitros method. Compared with the existing models, the new analytical method is simpler and more efficient.