We present the first 3D hydrodynamical simulations of ram pressure stripping of a disc galaxy orbiting in a galaxy cluster. Along the orbit, the ram pressure that this galaxy experiences varies with time. In this paper, we focus on the evolution of the radius and mass of the remaining gas disc, and compare it with the classical analytical estimate proposed by Gunn & Gott. We find that this simple estimate works well in predicting the evolution of the radius of the remaining gas disc. Only if the ram pressure increases faster than the stripping time-scale, the disc radius remains larger than predicted. However, orbits with such short ram pressure peaks are unlikely to occur in other than compact clusters. Unlike the radius evolution, the mass-loss history for the galaxy is not accurately described by the analytical estimate. Generally, in the simulations the galaxy loses its gas more slowly than predicted.