Mass transfer around a small eccentricity oblate spheroidal drop in a biaxial stretching and creeping flow, was investigated theoretically. The results at small capillary (Ca << 1) and large Peclet numbers (Pe >> 1), obtained via regular perturbations in Ca, suggest that: at very short times, the mass transfer rate to or from the drop represents, at O(Ca), mass transfer by diffusion only around a sphere. At long times or at steady-state, the mass transfer rate is, at O(Ca), slightly larger than that of a spherical drop, it increases with increasing the capillary number and decreases with increasing the viscosity ratio. Steady-state is established faster, as the viscosity ratio decreases and as the capillary number increases. Exact and approximate analytical solutions, valid at all times, which converge to the asymptotic solutions for short and long times, are also presented.