A theoretical analysis is presented of the flow field near a spherical fluid drop immersed in an incompressible Newtonian fluid which, at large distances from the drop, is undergoing an undisturbed flow. The undisturbed flows considered here are relevant to studies of drop motions near a phase boundary, and to some aspects of the coalescence of liquid drops. Exact solutions in closed form have been found using the harmonic function expansion in spherical coordinates. Calculation of the hydrodynamic force on the drop leads to generalization of Faxen’s law to a fluid particle in an arbitrary undisturbed creeping-flow. The solutions are then expressed in terms of the fundamental singularity solutions for Stokes flow in anticipation of future analysis of the drop coalescence. In addition, the deformed shapes are determined for a fluid drop freely suspended in an axisymmetric Poiseuillian flow.