The natural frequencies and the elastic buckling loads of square plates, containing reinforced square holes and subjected to inplane loads, are determined using the finite element method. The reinforcing beams which are located at the four edges of the hole are either square or rectangular in cross section. To determine the appropriate out-of-plane stiffness and mass matrices, a rectangular non-conforming bending element is employed. This element has three degrees of freedom at each of its four corner nodes. The finite element method is also used to calculate the inplane stress distribution prior to buckling. This inplane element is rectangular and is based on strain assumptions. The element also includes the inplane rotation as well as the two translational displacements as the three degrees of freedom at each of its four corner nodes. To model the behaviour of the reinforcement, a three-dimensional exact beam element is used. For this element, the degrees of freedom for out-of-plane displacement are consistent with the non-conforming bending element, and the inplane degrees of freedom are consistent with the inplane strain-based element. In the present paper the natural frequencies and the corresponding modes of vibration are investigated when the reinforced plates are subjected to uniform uniaxial, biaxial and shear loads. The variation of the natural frequencies with various sizes of reinforcement is obtained for plates subjected to a range of magnitude of inplane loading.