The continuous miniaturisation of solid-state devices and the proliferation of multilayer heterostructures in modern microelectronics, optoelectronics, and power electronics have placed epitaxial-layer quality at the centre of device-engineering research. A persistent obstacle in these systems is the lattice- and thermo-elastic mismatch between the substrate and the epitaxial layer, which gives rise to mismatch-induced stresses that degrade crystalline quality, generate threading dislocations, and ultimately limit device yield [1–3]. This article introduces and elaborates an approach aimed at decreasing mismatch-induced stresses in a heterostructure by subjecting the substrate to preliminary radiation processing before the gas-phase epitaxial growth of the active layer. The damaged near-surface region created by ionising radiation acts as a sacrificial defect reservoir whose recombination and accelerated diffusion during high-temperature Vapour-Phase Epitaxy (VPE) modify the local chemical potential and, in turn, the elastic state of the growing interface. To describe this coupled mass-and-heat-transfer problem, the present work develops an analytical framework based on the Method of Averaging of Function Corrections (MAFC), originally introduced by People and Bean [4]. The framework simultaneously accommodates spatial and temporal variations of the transport coefficients, the nonlinearity of the recombination kinetics of point defects and their complexes, and the coupling between the elastic, diffusive, and hydrodynamic fields. Approximate closed-form solutions are obtained to the second order of the MAFC iteration. The analysis indicates that preliminary radiation processing of the substrate may reduce the magnitude of the mismatch-induced stress by approximately 10–30 % for typical VPE conditions and simultaneously smooth the interface between the substrate and the epitaxial layer. The assumptions, the order of accuracy of the iteration, and the principal limitations of the framework are discussed in detail.