Unsteady mass transfer in the continuous phase around any axisymmetric drop of revolution at high Peclet numbers has been theoretically studied. General equations for the concentration profile, the molar flux, the concentration boundary layer thickness, and the time to reach steady state have been obtained using a similarity transformation and by the method of characteristics. Solutions for large number of problems can be immediately obtained, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop.