This paper focuses on the mechanical performances of the buried pipelines with functionally graded materials (FGM) subjected to strike-slip faults. A refined displacement function is introduced to derive the fault displacement and the strain distributions. The yield fault displacement is obtained by using the classical beam theory and the first yielding scheme. A finite element model is developed to verify the present derivations, and the verification indicates that the numerical results are in close agreement with the present analytical predictions characterized by the yield displacement and the strains, respectively. Finally, a parametric analysis is carried out to assess the factors that impact the performances of FGM pipelines, such as the diameter-to-thickness ratio of the pipeline, volume fraction exponent, fault inclination angles, the properties of the soil, and so on.