Wave propagation problems with radiation boundary conditions are non-hermitian and therefore typically cannot be solved by expanding in terms of We present a method for solving such problems entirely in terms of a superposition of normal modes, using the ''shifted eigenvalue'' method outlined by Lanczos. In effect, the desired system with an outgoing radiation boundary condition is coupled to a system which is identical, but has an incoming radiation boundary condition. The combined system is hermitian, and thus has real eigenvalues. We present numerical computations for a one-dimensional, semi-infinite, homogeneous continuum.