Abstract - Recent experiments show that upon abrupt start of a shear flow, a suspended drop undergoes an overshoot and undershoot in deformation if either the drop or the matrix is a polymeric fluid. Using a diffuse-interface formulation in two dimensions, we carry out numerical simulations that trace the origin of the transient to the mismatch of two time scales: a capillary time for drop deformation and a relaxation time for the polymers in the viscoelastic component. The results are in qualitative agreement with experiments.