Equilibrium distributions of misfit dislocation density along the growth direction of metamorphic buffer layers In x Al 1– x As/GaAs with maximum In content x max > 0.77 and different non-linear graded composition profiles are calculated. The effect of the initial In composition ( n = 2) of In x Al 1– x As buffer layer with convex-graded ( x min ) composition profile on misfit dislocation density as well as amount of residual stresses at its top part is considered. Using computational approach, it was shown that a dislocation-free region is formed under thin tensile- strained GaAs layer (1–10 nm) inserted into InAlAs metamorphic buffer layer, which agrees with experimental data obtained early by transmission electron microscopy. Novel non-linear graded composition profile of metamorphic buffer layer has been proposed, which results in twice reduction of misfit dislocation density as compared to the convex-graded one. In addition, equilibrium distributions of misfit dislocation density in the HEMT heterostructures with two-dimensional electron channel In x Al 1– x As, which are based on In 0 . 75 Ga 0 . 25 As/In 0 . 75 Al 0 . 25 As metamorphic buffer layer of various designs, are calculated. The values of inverse steps ( A ), representing the difference between the maximum In content of In x Al 1– x As ( x max ) and In content of In 0 . 75 Al 0 . 25 As virtual substrate, at which relaxation of the elastic strains in 2D channel In 0 . 75 Ga 0 . 25 As/In 0 . 75 Al 0 . 25 As doesn’t occur, are calculated for metamorphic buffer layers In x Al 1– x As with convex-graded and optimized non-linear graded composition profiles.