This paper presents a numerical study of the pure and eutectic alloy laser surface melting problem. The phase change is taken into account with a porosity-enthalpy formulation which permits the solution of the whole problem on a fixed cartesian grid. Thermocapillary convection modifies heat transfer and therefore the melted pool shape. The effects of experimental conditions such as laser scanning velocity and beam radius are analysed. The tested materials are pure aluminium and an aluminium alloy, which permit the study of both negative and positive surface tension-temperature gradients.