A 3-D transient model based on the numerical resolution of fluid-flow and the heat transfer equations is developped for deep penetration laser welding at high welding speed regime, whic results in the humping phenomenon. The physical mechanisms included in our model concern matter melting, vaporization inducing a recoil pressure and solidification. The implementation of developed procedures called User Defined Functions working interactively with the CFD Fluent code and a dynamic mesh method allowed us to treat the problem with specific and complex boundary conditions. As a result regular humps could be observed after resolidification on the weld seam.