The geometric irregularities of rail welds and polygonal wheels are common defects observed in high-speed railways, leading to the generation of high-frequency impact forces and vibrations in the wheel–rail contact system. This research establishes a novel vehicle-track coupled dynamic model that incorporates a 3D wheel–rail contact model using meshing grid and conjugate gradient methods to study the high-magnitude wheel–rail impact forces caused by rail weld irregularities and polygonal wheel combinations. The primary objective of this study is to develop a precise 3D contact model that incorporates the actual geometry of wheel and rail surface irregularities into the calculation of vehicle-track dynamic interactions. The study evaluates the effects of 3D rail weld irregularities and polygonal wheels on wheel–rail dynamic interaction by comparing results with those obtained from a conventional vehicle-track coupled model that considers a 2D contact model. The results show that the lengths and depths of polygonal wheels and rail weld irregularities, as well as vehicle speeds, significantly increase the wheel/rail dynamic impact forces. The results also indicate that the widening of irregularities not only significantly affects the wheel–rail contact force but also has an important influence on the contact stiffness.