We address theoretically the linear stability of a variable aspect ratio, rectangular plate in an uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.