Mass transfer in the continuous phase around a small eccentricity prolate spheroidal drop in an axisymmetric extensional creeping flow and at large Peclet numbers was investigated theoretically. The results show that, at very short times, the total quantity of solute transferred to or from the drop represents, at O(Ca1), mass transfer by diffusion only around a sphere. For long times, or at steady-state, the total quantity of solute transferred is, at O(Ca1), slightly smaller than that of a spherical drop, and it decreases with an increase of the capillary number or the viscosity ratio. (c) 2012 Canadian Society for Chemical Engineering