A study is made of the aerodynamics of wings executing simple harmonic oscillations. The wings considered are infinitesimally thin and slender; they may have longitudinal camber and curved leading edges. Leading-edge separation is simulated by an isolated line singularity of vortex type. The value of the reduced frequency is assumed to be such that Laplace's two-dimensional equation may be used as the governing partial differential equation. The determination of the flow then reduces to the solution of a simple problem in incompressible two-dimensional flow. The strength and position of the vortex and the generalised forces can be determined for an arbitrary wing by use of a Mercury Autocode programme. The modes of oscillation are assumed to be longitudinal, although bath rigid-body modes and modes of deformation can be calculated. Results have been obtained for a cambered delta wing, a flat ogee wing, and a flat gothic wing; the results for the last wing are in fair agreement with experiment.