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A semi-analytical model is first presented that thoroughly examines stress distribution patterns in inhomogeneous materials within a quarter space: a scenario of great significance and complexity observed in components such as rail-wheels, roller bearings, and gears. The model utilizes the Hetényi Image Method and Eshelby's Equivalent Inclusion Method, effectively handling the impact of inhomogeneities and satisfying the boundary conditions of the quarter space. To ensure efficient and accurate analysis, numerical techniques are incorporated, notably the Conjugate Gradient Method and the Discrete Convolution-Fast Fourier Transform algorithm. The model's validity and robustness are demonstrated through comparisons with the Finite Element Method results, displaying excellent agreement. Parametric analyses reveal that distance, depth to the free surfaces, and shape of the inhomogeneities significantly influence the results. The introduction of an edge decay coefficient, K e g , serves as a practical tool for rapid estimation of edge effects in inhomogeneous materials, significantly contributing to precise predictions of material fatigue and failure. [Display omitted] • The development of a semi-analytical model tailored for inhomogeneous materials within the quarter space is unveiled firstly. • The devised model integrates the merits of Hetényi Image Method and Eshelby's Equivalent Inclusion Method. • Leveraging the fast Fourier transformation and the Conjugate Gradient Method, the model ensures efficiency and precision. • A decay coefficient K e g is firstly proposed for a rapid estimation technique for the edge effects in inhomogeneous materials. [ABSTRACT FROM AUTHOR]