Two differential equations of moisture transfer based on the theory of moisture potential have been considered. The first equation includes the record of moisture transfer mechanisms of vapor and liquid phases and their relationship. The second equation is a simplified form of the first equation which makes it possible to apply a discrete-continuous approach. The peculiar properties of the boundary conditions setting of the outside air for temperature and humidity fields have been presented. It is proved that the use of the discrete-continuous method provides high accuracy of calculations and can be used in engineering practice to assess the unsteady humidity regime of enclosing structures. © 2021, ASV Publishing House. All rights reserved.