A model is suggested that describes stress relaxation in a nanowire with a finite-height cylindrical inclusion (quantum dot). The stress field created in the nanowire by such an inclusion is calculated. Two different mechanisms of stress relaxation in a nanowire with a cylindrical inclusion are proposed and analyzed. The first mechanism involves the formation of a prismatic misfit dislocation loop around the inclusion while the second mechanism suggests the formation of a penny-shaped crack in the inclusion cross section. It is shown that both mechanisms of stress relaxation can be realized in wide ranges of the structural and geometric parameters of the nanowire and inclusion. It is also demonstrated that in most cases the formation of a dislocation loop is more preferable than the formation of a penny-shape crack, although in some situations, crack generation becomes more preferable.