  We prove the nonexistence of finite time self-similar singularities in an
ideal viscoelastic flow in $R^3$. We exclude the occurrence of Leray-type
self-similar singularities under suitable integrability conditions on velocity
and deformation tensor. We also prove the nonexistence of asymptotically
self-similar singularities in our system. The present work extends the results
obtained by Chae in the case of magnetohydrodynamics (MHD).
