The absorption of moisture in a homogeneous, capillary active material obeys a diffusion law in which the driving potential is the volumetric water content, and the material behavior is characterized by the diffusivity function. In this study, an analytical solution for the one-dimensional case is proposed. The transient moisture profile is found by assuming the diffusivity as a multiple step function of the local water content and by solving the corresponding free boundary problem. Finally, a method for inverse determination of the diffusivity function is proposed. The case of a diffusivity function with three steps is investigated and discussed as an example.