Analytical results are presented for Rayleigh waves excited by a sudden change in the rate of growth of a subsurface zone of rupture. The curved rupture front advances across an inclined plane. The rupture can be brittle or cohesive tractions can act at its front. The analysis consists of two parts: First, ray theory is used to calculate wavefront approximations to the waves emitted when the rupture front speed suddenly changes. Secondly, a representation integral for the Rayleigh wave, where the integration is performed over a surface enclosing the rupture front, it constructed by using the emitted waves in combination with an appropriate Green's tensor. This integral is evaluated asymptotically. Synthetic accelerographs are constructed which illustrate how the rupture process, and the geometry of the rupture front and the fault plane affect the excitation of Rayleigh waves.