An approximate analytical 2-D solution for the strain field components e11, e12 and e22 occurring in a cubic material due to a coherently bonded shear eigenstrained inclusion of cylindrical geometry was obtained by means of Continuous Fourier Transforms (CFT). A Discrete Fourier Transform (DFT) based numerical model was used in order to test the validity of the results. For the case where the cylindrical inclusion and the surrounding media are elastically homogeneous and the orientation of their principal crystal axes are the same, a correlation between the analytical and numerical models is demonstrated, both for strongly and weakly anisotropic materials. Moreover, the strain fields within the inclusion are shown to be of homogeneous isotropic type. Finally, an expression for the closed-form strain energy of two cylindrical inclusions at arbitrary radius and angle was derived, and then used to determine the minimum energy configuration for the system.