We present the results of a numerical study of helium detonations on the surfaces of neutron stars. We describe two-dimensional simulations of the evolution of a detonation as it breaks through the accreted envelope of the neutron star and propagates laterally through the accreted material. The detonation front propagates laterally at nearly the Chapman-Jouguet velocity, v=1.3×109 cm s-1. A series of surface waves propagate across the pool of hot ash behind the detonation front with the same speed, matching the speed expected from shallow water wave theory. The entire envelope oscillates in the gravitational potential well of the neutron star with a period of ~50 μs. The photosphere reaches an estimated height of 10 km above the surface of the neutron star. Our study confirms that such a detonation can insure the spread of burning over the entire neutron star surface on a timescale consistent with burst rise times. We analyze the sensitivity of the results to the spatial resolution and the assumed initial conditions. We conclude by presenting a comparison of this model to type I X-ray bursts.