Recent experiments show that upon abrupt start of a shear flow, a
suspended drop undergoes an overshoot in deformation if either the
drop or the matrix is a polymeric fluid. Using a diffuse-interface
formulation, we carry out two-dimensional 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.