Convection-dominated melting in a rectangular cavity is analyzed numerically with particular attention to the multi-cellular flows in the melt. At the earlier stage of the melting, the melt region is quite similar to a cavity with high aspect rati71, where the multi-cellular natural convection appears. Numerical results show that the formation and evolution of the multiple flow cells in the melt region is approximately similar to t]tat of a single-phase flow in a tall cavity with the same aspect ratio; however, the continuous change of the melt region due to the melting affects the detailed process. Also, numerical aspects for the prediction of the detailed flow structure in the melt are discussed.