The controlled release of over-loaded drug in a plate-like polymer matrix, the Higuchi's problem, is investigated theoretically. Taking the advantage of Landau transformation, we restore the concentration profile of drug in a polymer matrix, the rate of release of drug from the polymer matrix, and the temporal variation of location of the moving boundary taking the external mass transfer resistance into account. The applicability of the series of moving boundaries, a numerical approach often adopted, is examined. We found that it may become ineffective when the over-loading of drug in a polymer matrix is too small. In contrast, our method has no such limitation. We conclude that assuming the transfer of drug to occur at a pseudo-steady-state condition is inadequate if the degree of over-loading for drug is low or the external mass transfer resistance is significant.