The radiation pressure is calculated for a surface which is moving in an electromagnetic radiation field that is isotropic to a rest observer. In the limit where the velocity of the surface is that of light, the pressure is found to reach a maximum value 2u, whereuis the isotropic electromagnetic energy density for the observer at rest. The finite value comes with an integration over radiation incident at all angles, even though radiation from a source which is directly approaching the surface has infinite momentum when the surface velocity reaches the speed of light. Estimates of radiation pressure in interstellar space lead to the result that the energy expended by a space-traveling vehicle in moving against electromagnetic radiation, at any possible speed, would be negligible.