Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non-zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006; 96: 134503; Subramanian and Koch, Phys Fluids. 2006; 18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow-gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier-Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233-240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow-gradient plane. However, the wake near the flow-gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 1419-1433, 2011