Pipelines related to industrial supplies such as oil or gas are a key part of modern development, so it is important to ensure their appropriate response to a seismic action. The same applies to drainage or water supply in contemporary cities. Structural analysis of pipelines is a well-established topic in engineering practice. In this paper, we will present the application of the methodology Proper Generalized Decomposition (PGD) to the numerical analysis of buried pipelines, in order to obtain a parametric solution based on material properties. A new well-established method to compute the safety of buried pipelines when crossing faults is develop, based on a 3D finite element approach for computing a fine enough solution while circumventing the difficulties related to the excessive degrees of freedom of fully 3D mesh-based discretization, we took advantage of in-plane-out-of-plane separated representations within PGD. Those results can be used to safety evaluation, maintenance and protection of buried pipelines crossing fault area. The solution can be evaluated in real-time from the offline construction of a parametric solution to the associated problem within the PGD framework.