In the existing literature, the contact pressure at the armature-rail interface was typically assumed to be an ideal contact in a three-dimensional transient model. Nevertheless, contact pressure distribution at the armature-rail interface during the launching process, induced by the interference fit between the rail and C-shaped armature, is non-uniform and can be influenced by the armature structural parameters. The armature structural parameters subsequently influence current density distribution and the Lorentz force distribution. A three-dimensional transient electromagnetic model of the electromagnetic railgun considering non-ideal contact pressure distribution at the armature-rail interface is established. To analyze the temporal evolution of electromagnetic fields during the launching process, the finite element method is utilized to perform simulations. Subsequently, the Lorentz force, the muzzle velocity, and the inductance gradient can be obtained. The variations of the armature tail thickness, the armature tail splay angle and the interference amount of armature structural parameters are taken into account to investigate the influence on the contact force, maximum contact pressure, and proportion of effective contact area at the armature-rail interface. Then, these current with variable density distribution and the resistive force acting on the armature exhibit negligible effect on muzzle velocity and inductance gradient. It can be concluded that this paper provides a theoretical basis for optimizing armature structural design, predicting rail endurance, and advancing launch dynamics modeling.