The first detailed numerical investigation on the mass and heat transfer both outside and inside a solid or liquid sphere immersed in a simple extensional flow for a larger range of Peclet numbers (1100,000) is presented. By making use of the known Stokes velocity field at small Reynolds numbers, a finite difference method with the control volume formulation is adopted to solve the convection-diffusion transport equation. Simulation results show that the transport rate, which is represented by Sherwood number, is significantly affected by Peclet number and viscosity ratio. The flow direction, no matter a uniaxial extensional flow or a biaxial extensional flow, has no effect on the total transport rate but affects the concentration distribution a lot. Some comparisons between present simulations and previous studies are made to validate each other and confirm the reliability and applicable scopes of reported correlations. A few new correlations are put forward to predict the transfer rate at finite Peclet numbers for various values of viscosity ratios. (c) 2011 American Institute of Chemical Engineers AIChE J, 58: 32143223, 2012