Damage to the overlying soil caused by fault misalignment poses a significant threat to the structural safety of buried pipelines crossing faults, which is a non-negligible factor in the design of underground pipelines in complex environments. Existing research rarely involves analytical solutions for the force and deformation of pipeline structures under normal and reverse fault movements, and theoretical studies on fault-pipeline interactions often treat the pipeline structure as continuous, with little consideration for the influence of pipeline joints. Firstly, soil displacement curves for both normal and reverse faults are derived using the erf and erfc functions, based on a simplified SSR (stationary zone, shearing zone, rigid body zone) soil deformation model. Secondly, the deformation and internal force of the buried pipeline structure are solved using the two-parameter Pasternak foundation model and the finite difference method. Finally, the theoretical analytical solution is compared with existing experimental and 3D numerical simulation results, showing good agreement. In addition, sensitivity analyses are conducted for key physical parameters, including fault dip, fault-pipeline inter location, and joint rotation stiffness. The results show that fault dip will change the position of the pipeline displacement curve and axial stress curve, but the maximum displacement and maximum axial stress are basically identical. The inter of the fault and the pipeline will not only change the shape of the pipeline displacement curve and axial stress curve, but also alter the maximum axial stress. With the increase of joint rotation stiffness, the maximum axial stress value of the pipeline increases. When the joint rotation stiffness is large enough, the jointed pipeline can be calculated as if it is continuous.