AbstractThis paper is concerned with the time‐dependent deformation of a spherical capsule suspended in a viscous fluid. The basic assumptions are that (a) the flow in the fluid regions is governed by the Stokes' equations, (b) the deformation is small, and (c) the membrane is purely elastic. Condition (b) requires either the elastic time scale to be small in comparison with a characteristic flow time (i.e., a sufficiently stiff membrane and/or a sufficiently weak flow field) or the inside fluid to be highly viscous. It also allows us to employ a linearly elastic constitutive equation for the membrane, as first approximation. The general results obtained are compared with corresponding results for surface tension droplets. The case of sedimentation in a quiescent fluid, a capsule freely suspended in a linear flow field, and steady‐state results for quadratic flow fields (with emphasis on circular Poiseuille flow) are stud