AbstractA problem of transient heat transfer driven by high heat flux is solved numerically by a boundary integral equation method (BIEM). This problem is a model of thermal phenomena in plasma facing components under normal and off-normal conditions in fusion reactor, and it includes radiation heat transfer, melting, solidification, evaporation and convective cooling. The solutions obtained by the BIEM show qualitative agreement with the reported experimental and numerical results of an electron beam heating test. It demonstrates the validity of the BIEM. The characteristics of the BIEM, such as the allowance of use of rather large time step and coarse discreitzations, are shown.