The image force on a screw dislocation at the distance $$\rho =\alpha a\,(\alpha >1)$$ from the tip of an isotropic wedge of shear modulus G with a circular inhomogeneity of radius a and shear modulus $$G'$$ at its end is determined by the method of image dislocations. If the wedge angle is $$\pi /n$$ , for an integer $$n\ge 1$$ , $$4n-1$$ image dislocations are needed to achieve the required traction-free boundary conditions and the interface continuity conditions. It is shown that for the positive values of the inhomogeneity parameter $$\kappa =(G'-G)/(G'+G)$$ , there is an equilibrium position of the dislocation along the plane of symmetry of the wedge, specified by the parameter $$\alpha _\mathrm{eq}=\left[ 2n\kappa +\left( 1+4n^2\kappa ^2\right) ^{1/2}\right] ^{1/2n}$$ . The equilibrium position is stable relative to disturbances of the dislocation position along the plane of symmetry, but unstable for other disturbances. If the edges of the wedge and the inhomogeneity are fixed, rather than traction free, the equilibrium position of the dislocation along the plane of symmetry is specified by $$\alpha _\mathrm{eq}=\left[ 1-4n\kappa /(2n-1)\right] ^{1/4n}$$ , provided that the inhomogeneity is softer than the matrix material ( $$\kappa <0$$ ). The equilibrium position is unstable relative to disturbances of the dislocation position along the plane of symmetry. In the case of homogeneous wedges ( $$\kappa =0$$ ), the image force in the plane of symmetry for a wedge with fixed edges depends on the wedge angle and is given by $$f=(2n-1)k/2\rho$$ (away from the tip), while for a wedge with free edges the image force is independent of the wedge angle ( $$f=-k/2\rho$$ ).