An approach is presented to study dynamical buckling of stiffened plates. The stiffened plate is divided into one plate and some stiffeners, with the plate analyzed based on the classical thin plate theory, and the stiffeners taken as Euler beams. Assuming the displacements of the stiffened plate, the Hamilton principle and modal superposition method are used to derive the eigenvalue equations of the stiffened plate according to energy of the system. Finally, numerical examples of simply supported stiffened plates are presented to study the critical loads with the initial geometrical imperfection considered. Detailed discussion on how the initial geometrical imperfection, the number and the flexural rigidity of stiffeners influence the critical load is carried out. The results show the 1st mode shape of the initial geometrical imperfection has a great effect on the critical load, and the increase of the number and the flexural rigidity of stiffeners can strengthen the dynamical buckling capacity. These conclusions can also provide references for engineering design.