In this study the Green's function technique has been used to solve the solidification problem in plate geometry for three alternative types of boundary condition at the surface of the plate. With this method the differential equation for heat conduction is transformed into an integral equation with line integrals, reducing in this manner the integration to a solution at the boundaries of the domain. The advantage is a considerable saving of computer time. Simple forms of boundary condition, that is constant values of temperature T-0, of heat flux density q(0), or of heat transfer coefficient it, are used, but the treatment can readily be extended to time dependent values. The rate laws for the advancement of the solidification front and for the evolution of surface temperature (in the case of prescribed q(0) or h) are obtained and are presented in non-dimensional form.