We use a front-tracking method to simulate inward solidification in a cylindrical container with volume change. The problem includes temporal evolution of three interfaces that meet at a triple point. The governing Navier-Stokes and energy equations are solved for the whole domain, setting the velocities in the solid phase to zero and with the non-slip condition on the solid-liquid interface. Computational results show that a cavity forms in the center of the cylinder if the density of solid is higher than that of liquid, i.e. rho(sl)>1.0. In contrast, if rho(sl)<1.0, the solidified product has a conical shape in the central region of the cylinder. The triple point also affects the solidification process as an increase in the growth angle results in a decrease in the cone angle at the top in the case of volume expansion.