Axisymmetric thermocapillary convection during laser melting has been investigated numerically. The dynamic free surface, with pinned contact point at the edge of the molten pool, is obtained as a solution of the coupled transport equations. Free surfaces at the steady state are depressed at the center and convex near the edge of the molten pool because fluid flows away from the center. The surface deformations decrease with increasing Re at fixed Ca, while they increase with increasing Ca at fixed Re. The width and depth of the pool, temperature and surface deformation increase with increasing Bf. At the transient cases, the size of the pool and surface deformation increase monotonically with time. The shape of the free surface is a bowl bump at a low Re, while at a high Re two kinds of surface shapes occur with time: bowl and Sombrero-shaped bumps. (C) 2004 Elsevier Ltd. All rights reserved.