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The one-dimensional time dependent heat conduction equation for surface heating and a phase boundary (the so-called classical Stefan problem) has been solved in the absence of vaporization. For a rectangular laser pulse and constant material parameters, useful solutions have been determined for melt depth as a function of time both during and following the pulse. Based on the model, the intensity dependence of the melt depth is investigated. Two melting regimes—slow and fast—have been identified by comparison with previously reported data for silicon.