In the diffusion boundary layer approximation an exact analytical solution is obtained for the problem of unsteady convective mass exchange between a spherical droplet (bubble) and an arbitrary three-dimensional linear shear flow, with the unperturbed velocity field assigned by the symmetric shear tensor. The dependence of Sherwood number on time and Peclet number is established. A simple approximate formula is presented for calculating the rate of unsteady mass exchange of droplets and solid particles with an arbitrary steady flow. The stationary problem of mass exchange between a droplet and a linear shear flow in the presence of the first-order volumetric chemical reaction is considered. An equation is suggested to compute the Sherwood number for a droplet or a particle of arbitrary shape and for any type of flow at large Peclet numbers over the entire range of reaction rate constants.