The buckling and post-buckling behavior of initially imperfect, sinusoidally curved hinged-hinged beams undergoing very large deflections subjected to lateral concentrated loads acting at the midpoints is investigated via the geometrically nonlinear analysis of the problem. The transverse shear deformation is neglected. The amplitudes of the imperfection are considered to be relatively small. Therefore, the concerning curved beams (or arches) are shallow. The values of the extensional rigidity/length of the beams are assumed to be large enough not to permit considerable amount of change in the lengths of the beams during the deformation. The force-deflection curves corresponding to various amplitudes of the imperfection and the diagrams of the deflections and internal forces corresponding to various stages of the deformation, including those after the buckling, are presented. Not being able to solve the highly nonlinear problem analytically, numerical methods are used.