Extensive experimental work has shown that pulsed laser micro polishing (PLP) is effective for polishing micro metallic parts. However, the process physics have not been fully understood yet, especially with respect to the melt pool flow. A reliable physical model can be of significant assistance in understanding the fluid flow in the melt pool and its effect on PLP. In this paper, a two-dimensional axisymmetric transient model that couples heat transfer and fluid flow is described that was constructed using the finite element method. The model not only provided the solutions to the temperature and velocity fields but also predicted the surface profile evolution on a free deformable surface. The simulated melt depth and resolidified surface profiles matched those obtained from optical images of PLPed Ti6Al4V sample cross-sections. The model was also used to study the effect of laser pulse duration on the melt pool flow. The study suggests that longer pulses produce more significant fluid flows. The cut-off pulse duration between capillary and thermocapillary regimes, below which minimal Maragoni flow should be expected, was estimated to be 0.66s for Ti6Al4V, which also matched well with the experimental results. It is evident that the coupled model offers reliable predictions and thus can be extended for a more complex parametric study to provide further insights for PLP.