To understand the vertical and the lateral growth mechanisms of microchannel epitaxy (MCE) in detail, two-dimensional numerical calculation is carried out employing the different boundary conditions on the top and the side surfaces of the MCE island. By solving a two-dimensional diffusion equation, a concentration profile of the solute is determined as a function of growth time. By calculating the lateral growth rate, the width-to-thickness ratio of the MCE island (W/T ratio) has been derived from the computation. The calculated W/T ratio shows a good agreement in both cooling rate and growth temperature dependence with those obtained from the experiment when the growth temperature is above 500 degrees C.