Advanced calculating models have become an essential tool in building physics practice for the prediction of thermal and hygric performance of building envelopes. Successful application of any simulation model is generally affected by the mathematical model on which it is based, the quality of the input data, and, finally, when sensitivity and efficiency of the calculations are to be investigated—the numerical method itself. Simulation of the rapid moisture transfer through a building envelope is a typical process that encounters numerical difficulties. The problem is mostly related to certain building materials, such as bricks, characterized by their low moisture capacity and high hydraulic conductivity in the moisture-saturated region. This paper investigates three numerical techniques for the estimation of the moisture transport coefficients during such processes. Two of them— the harmonic and the linear techniques—are widely used, whereas the integral one is not. It is shown that numerical difficulties can be overcome by choosing a suitable technique.