The two-dimensional Laplace integral transform technique is used to solve the problem of melting a semi-infinite target induced by surface absorption of a laser pulse. Mathematical expressions for the temperature distribution within the solid part of the target and the thickness of its liquified part were obtained considering cooling, temperature dependent absorption coefficient of the irradiated surface and constant temperature in the molten layer. As an illustrative example computations were carried out on a semi-infinite aluminum (Al) target.