The crux of the present work is to come up with a geometrical and mathematical model, that is oriented towards investigating the impacts of non-homogeneity as well as planar and non-planar boundaries on the displacement components (DCs) of Rayleigh-type wave (RTW) propagating in a pre-stressed nearly incompressible elastic half-space. The methodologies that are applied to establish the expressions for DCs and frequency relation include variable separable technique, Taylor’s series expansion as well as substitution method. Considering the planar free surface of the non-homogeneous pre-stressed nearly incompressible elastic half-space (NHPSNIEHS), the frequency relation of RTW is derived, which as a special case, concurs well with the established results in the literature. The numerical simulation pertaining to DCs of RTW is executed, and their reliance on wave number, non-homogeneity, hydrostatic stress and principal Cauchy stress are figured out. Also, the existence domain of RTW in NHPSNIEHS without non-planar boundary is manifested graphically. Additionally, a comparative approach between NHPSNIEHS and its corresponding homogeneous pre-stressed nearly incompressible elastic half-space (HPSNIEHS) for RTW is accomplished for the aforementioned affecting parameters associated with the considered model. The computational results reveal that the existence of non-homogeneity in the half-space has notable influence on the propagation behavior of RTW.