This thesis examines how finite element shape functions and refinement strategies affect the numerical simulation of pantograph–catenary interaction, with focus on the prediction of contact force and the related computational cost. The study is based on an Euler–Bernoulli beam representation of the catenary and compares standard element refinement with polynomial enrichment of the beam shape functions. The contact between the pantograph and the catenary is modelled through a penalty-based formulation, while the dynamic response is integrated in time using the Newmark method. The first part of the work develops and validates the finite element model in comparison to analytical results for the rigid catenary and fot the semi-analytical benchmark proposed by Collina and Bruni for the moving-mass contact problem.