A new solution to the problem of flexural vibration of an infinite wedge excited by a point harmonic load is obtained via a superposition of the geometric and diffraction fields, for simply supported and roller boundary conditions along the edges. The diffraction integrals are evaluated both in closed form in terms of the Faddeeva function and also as an asymptotic series using the steepest descent method. An eigensolution is also derived by expanding eigenfunctions in the angular direction and propagation terms in the radial direction. These two representations of the solution are compared numerically for accuracy and spatial distribution in different frequency regimes. The relative contribution of the geometric and diffraction fields to the overall solution is examined. This result is then compared to the second-order Helmholtz wave equation solution in order to demonstrate the near-field effects arising due to the fourth-order biharmonic formulation. The authors’ motivation for obtaining the solution for a wedge-shaped infinite plate is that it is an essential step toward devising numerical models for the vibration of arbitrary polygonal plates. By combining the contribution from diffraction at the vertices of a polygonal plate with the geometrical solution obtained by the method of images, the authors expect to obtain better predictions at mid and high frequencies than is possible by other available methods.