The drag coefficients for a prolate ellipsoid moving along its axis of symmetry, in the creeping flow regime, either towards or away from a plane surface are calculated. The plane surface may have either a no-slip boundary condition, corresponding to a solid wall, or a perfect slip condition, corresponding to a free surface. First the analytical solutions are employed to obtain exact values for the full range of feasible particle-plane gaps. Next, simple exact formula for the asymptotes at small and large gaps are presented. Finally, some convenient approximate formula are obtained that may be used across the full range of gaps. Crown Copyright (C) 2014 Published by Elsevier Ltd. All rights reserved.