In the context of the global transition to the circular economy principles, arbolite as a composite material with a high content of secondary organic resources is of particular importance. However, the arbolite widespread usage is hindered by the insufficient study of non-stationary heat and mass transfer processes during the raw blocks drying, which leads to structural defects formation and product quality decrease. The purpose of this work is to develop a mathematical model of moisture transfer in arbolite products for three drying schemes: on the permeable, impermeable, and partially permeable base. Based on the nonlinear diffusion equation for capillary-porous media, an analytical solution of the non-stationary mass conductivity problem was obtained for an uneven initial moisture distribution and second-kind boundary conditions using the Fourier and Kirpichev dimensionless criteria. The microprocess method allowed for the consideration of the mass flows temporal non-stationarity at the computational domain boundaries with an approximation error of no more than 3–5%. The modeling showed that drying on the impermeable base forms the asymmetric moisture profile with a maximum in the bottom zone, increasing the shrinkage defects risk, while the partially permeable flooring scheme reduces the drying time by 25–30% with maintaining structural homogeneity. The proposed model provides a basis for optimizing thermal treatment modes and developing a digital twin for the production of arbolite products.