<p>Using complex variable techniques, we derive an analytical solution to the problem associated with a four-phase composite consisting of two jointed half-planes each containing a circular elastic inhomogeneity subjected to uniform remote anti-plane shear stresses. Firstly, a conformal mapping function is introduced to map the corresponding (two circular and one planar) interfaces onto three concentric circles in the image plane. Secondly, a general solution for the four analytic functions is obtained in terms of a single unknown analytic function by imposing the continuity conditions of traction and displacement across the three perfectly bonded interfaces. Thirdly, an explicit expression for the single analytic function is established by considering the imposed uniform remote loading. Finally, the elastic fields of stresses and displacement in the four-phase composite are completely determined. Numerical results are presented to demonstrate the theory. Analytical solutions are also derived for an arbitrary singularity applied at any position in the four-phase composite.</p>