As the first step toward developing a generic model for the acoustically radiating vibrational modes of the violin and related instruments, the modes of both freely supported and edge-constrained top and back plates have been investigated as functions of shape, arching height, elastic anisotropy, the f-holes and associated island area, thickness graduations, and the additional boundary constraints of the ribs, soundpost, and bass-bar present in the assembled instrument. Comsol shell structure finite element software has been used as a quasi-experimental tool, with physical and geometric properties varied smoothly, often over several orders of magnitude, allowing the development of the plate modes to be followed continuously from those of an initially square plate to those of doubly-arched, guitar-shaped, orthotropic plates and their dependence on all the above factors.