This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities.Based on the semi-analytical method(SAM)and the equivalent inclusion method,numerical procedures were developed and the effects of inclusion shape and distribution were analyzed.Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress.Interactions of inter-inclusions and inclusion-matrix were taken into account.Numerical results showed the presence of inhomogeneities(i.e.,microstructures in solids)indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions.The effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions.The physical significance of this study is to provide an insight into the relation between the material microstructure and its response to the external load,and the solution approach and procedures may find useful applications,for example,the analysis of fatigue and crack propagation for composite materials,prediction of stress field in solids containing material defects,and study of the mechanism of chemical-mechanical polish(CMP)for inhomogeneous materials,etc. This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities. Based on the semi-analytical method (SAM) and the equivalent inclusion method, numerical procedures were developed and the effects of inclusion shape and distribution were analyzed. Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress.Interactions of inter-inclusions and inclusion-matrix were taken into account. Numerical results showed the presence of inhomogeneities (ie, microstructures in solids) indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions. effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions The physical significance of this study is to provide an insight into the relation between th e material microstructure and its response to the external load, and the solution approach and procedures may find useful applications, for example, the analysis of fatigue and crack propagation for composite materials, prediction of stress field in solids containing material defects, and study of the mechanism of chemical-mechanical polish (CMP) for inhomogeneous materials, etc.