The rate of transfer of a solute between a single drop, rising or falling at intermediate drop Reynolds numbers (10 less than or equal to Re less than or equal to 250), and a continuous liquid phase, has been predicted by the solution of the fundamental fluid flow and mass transfer equations. The equations of motion are satisfied by use of the method of weighted residuals, assuming particular forms of the stream functions for both phases. The derived velocity profiles are then simplified for the region near the drop interface and introduced into the diffusion equation. This is solved analytically, after simplification, by a transformation of variables to a form that applies only for short distances on either side of the drop surface. Concentration profiles and mass transfer coefficients for both phases are obtained in the form of analytical expressions. Predicted values of the bulk concentrations in the dispersed phase and mass transfer coefficients compare favourably with available experimental data, though the latter were unreliable.