The hydrodynamic force on a body that undergoes translational acceleration in an unbounded fluid at low Reynolds number is considered. The results extend the prior analysis of Lovalenti and Brady [to appear in J. Fluid Mech. (1993)] for rigid particles to drops and bubbles. Similar behavior is shown in that, with the inclusion of convective inertia, the long‐time temporal decay of the force (or the approach to steady state) at finite Reynolds number is faster than thet−1/2predicted by the unsteady Stokes equations.