Quantum wires (QWs) and quantum dots (QDs) have been widely applied in semiconductor devices due to their excellent mechanical, electronic, and optical properties. Faux and Downes [J. Appl. Phys. 82 (1997) 3754–3762] have obtained the closed-form solutions for strain distributions produced by QWs, whose cross section is composed of any combination of line elements and circular arcs. In this paper, Eshelby's inclusion model is established to simulate QWs and the closed-form solutions for the resultant displacements are obtained. By employing the method of Green's function, the displacement solutions may be formulated as area integrals and then converted into contour integrals along the boundary of the QW. The present study complements Faux and Downes' work and provides an efficient shortcut for analyzing the displacements of a QW, whose boundary may be discretized into line segments and circular arcs.