The reverse vortex street differs from the ordinary Karman vortex street in the direction of the rotation of the vortices. Such a street is formed behind the oscillating airfoils in the flow. It is of interest in connection with studies of the aerodynamics of flapping wings. It is known that the vortex wake behind a symmetric airfoil performing symmetric oscillations in a certain range of parameters becomes asymmetric, which leads to the appearance of a nonzero average lift. Reasons of the symmetry violation are associated with the instability of the reverse vortex street, but the mechanism of this instability is currently not well understood. In this work, the analysis of the stability of the reverse vortex street is carried out on the basis of the theory developed by Karman for infinite rows of point vortices. In contrast to the Karman model, in this work, semi-infinite rows with periodically arising new vortices at their ends are considered. This is the first time this model has been used. It is shown that the periodic appearance of new vortices radically affects the characteristics of the street stability. It is found that the violation of the symmetry of the reverse vortex street is associated with its instability to bending perturbations, while the ordinary Karman vortex street behind the body is unstable to varicose perturbations. Regions of instability are determined.