This paper presents a parametric study of the stresses in a matrix near a cylindrical inclusion. The Texas Grain Analysis Program (TEXGAP), a finite element approach, is used to model the problem. Eight different models are investigated which establish the stress effects of varying interlayer thickness, varying modulus of elasticity of inclusions and interlayers, and element size. The results, presented as plots of axial stresses, show a definite lowering of the stress in the area of inclusion termination as the interlayer thickness is increased from zero. A further stress decrease is noted with the addition of some inclusion elasticity. Similarly, the stresses also decrease as the interlayer becomes more elastic.