Theoretical predictions for the 3D shape of a Newtonian drop immersed in a Newtonian fluid under slow flow have been available for a long time (C.E. Chaffey and H. Brenner, J. Colloid Interface Sci. 24, 258 (1967); J.M. Rallison, J. Fluid Mech. 98, 625 (1980)). The predictions contain four scalar coefficients, given in terms of the viscosity ratio of the component fluids. In this work, experimental values of such coefficients were measured for the case of two Newtonian fluids in simple shear flow. The experiments were carried out in a parallel plate apparatus, equipped with video-enhanced microscopy, and the measurements were performed by image analysis techniques. The results were also compared to theoretical calculations and provide the first complete assessment of shape predictions for the case of Newtonian fluids. Copyright 1999 Academic Press.