A method for the simulation of dynamic vehicle–track interaction and evaluation of measures to improve the design of railway crossings is presented. To accurately represent the high-frequency dynamics and non-linear contact conditions of the vehicle–track system, the vertical interaction between a wheelset and the crossing is simulated in the time domain using a Green's function approach based on extensive finite element models of track and wheelset in combination with an implementation of Kalker's variational method to solve the non-Hertzian, and potentially multiple, wheel–rail contact. Both wheels of the wheelset in simultaneous contact with the crossing rail and the outer rail are considered. Rigid and flexible wheelset models are compared. The sampled contact geometry of the crossing, including the discrete irregularity between the wing rail and the crossing nose, is used to determine a three-dimensional surface geometry between each pair of adjacent rail cross-sections. A parameter study is performed to investigate the influence of crossing design on the maximum vertical wheel–rail contact force and the contact pressure generated at the sleeper–ballast interface. It is concluded that a design with a combination of increased sleeper width, softer rail pads and implementation of under sleeper pads (USP) will reduce the track stiffness gradients in the crossing panel and mitigate the risk of differential track settlement by lowering the sleeper–ballast contact pressure. © 2019