The propagation of waves in a previously deformed elastic membrane is investigated. The membrane is considered as a simple two-dimensional continuum, thus neglecting the dispersive effects of finite thickness. The strain-induced anisotropy of wave propagation is represented by slowness and ray curves. The three branches of each of these curves correspond to one flexural wave and two in-plane deformation waves. The intensity of an acceleration wave is governed by a transport equation, i.e., an ordinary differential equation valid along the rays of the propagating wave front. Its closed-form solution is presented for the case of a flat membrane subjected to an arbitrary homogeneous deformation.