A rigid-plastic finite element method combined with the effect of elastic deformation is proposed. In the present method, elastically and elastic-plastically deforming elements are mixed with rigid-plastically deforming elements in the deforming material. In this formulation based on an implicit scheme, the nodal forces for the rigid-plastic elements are equilibrated with those for the elastic and elastic-plastic elements at the end of each deformation step. The nodal forces for the elastic and elastic-plastic elements are derived by considering the effect of rigid-body rotation during deformation increment. The elastic-plastic element is transformed into the rigid-plastic one during the loading when the elastic strain increment is small. The reverse transformation is carried out in the unloading. This leads to a comparatively small computing time and the improvement of the calculated results. Plane-strain bending of a plate with a round punch is simulated by the present method under a mixed condition of elastic, elastic-plastic and rigid-plastic elements in the plate. Deformation behaviour in early stages of bending is successfully calculated. The calculated amounts of springback are in reasonable agreement with the experimental ones for aluminium plates because the stress distribution in the elastic regions without achieving yielding around the edges of the plate is taken into consideration.