The paper studies the influence of imperfect contacts (IC) at the phase interfaces of a micro-heterogeneous material on the macroscopic transport of impurity and the stress-strain state caused by its accumulation. Two types of IC are considered: segregation, which involves the accumulation of impurity that disrupts the continuity of concentration, and the formation of bypass paths for accelerated diffusion, which disrupts the continuity of the normal component of the flux. Modeling the coupled processes of mass transport and changes in the stress-strain state of the medium consists of two stages. In the first stage, the effective diffusion permeability of the material is determined using micromechanical methods. In the second stage, the macroscopic elasticity problem caused by mass transport is solved. The analysis is carried out using the example of a long cylinder, which is a two-phase material at the micro-level, consisting of a matrix and less permeable prolate spheroidal inhomogeneities with an arbitrary distribution of orientations.