The analysis of the velocity skin effect (VSE) in electromagnetic launchers (EMLs) requires a 3-D transient finite element method, unlike magnetic skin and proximity effects. However, VSE is dominant at high speeds, and this creates convergence problems when moving or deformed mesh physics is used in a transient FEM in the 3-D analysis. Commercial finite element software cannot solve the electromagnetic aspects of such a high-speed application with a transient solver in 3-D. Although 2-D approximations can be used, such an approximation overestimates VSE resistance due to geometry simplifications. In this study, we proposed a novel quasi-transient 3-D FEM model where the air-armature region's conductivity is varied to emulate the high-speed motion of the armature. Results showed that the 2-D approximation overestimates the VSE resistance by almost 40%. The proposed VSE model has been included in the EML model, and simulation results are compared for experimental results with different EMLs, EMFY-1, and EMFY-2 and showed good agreement.