Because of the differences in temperature which are present in the melt, convection usually appears. Convective heat transfer directly influences the position of the solid-liquid interphase. Numerical simulation of melting of pure substance in rectangular two-dimensional cavity is presented in this work. Melting is observed from the moment when one side wall's temperature is set above melting point. Besides the front position, velocity field, temperature field and Nusselt number are also observed. The control volume method with non uniform fixed grid is used for the calculation. It is based on the continuum (one-phase) model which defines space dependent phase fraction function.