Degenerated shell element and membrane element have been widely applied in thin sheet metal forming analysis. However, for medium thick plate metal forming, especially in the case of typical double-sided contact problems such as local bulge forming or pure bending with a small radius, these two element models cannot accurately simulate normal extrusion deformation of the sheet metal. In this paper, a new finite element (FE) solver based on the solid-shell element dynamic explicit algorithm and implicit algorithm is developed for the simulation of medium thick plate metal forming and springback. The solid-shell element model considers bending effects with a thickness-direction multiple-point integration approach. The viscous damping hourglass control algorithm eliminates the spurious deformation modes activated by in-plane reduced integration (RI). The double sided contact analysis considering thickness variation describes the extrusion deformation in the thickness direction accurately. An improved plane-stress constitutive model in co-rotational configuration together with Hill's quadratic anisotropic yield criterion is employed to update the stress field. The solid-shell element obtains both solid-like and shell-like behaviours to simulate large membrane deformation, shear deformation and rotation. To test the performance of the solid-shell element, some numerical examples are taken and compared with experiments. The comparison results demonstrate that the solid-shell element model is competitive enough in the simulation of medium thick plate metal forming and springback.