  We construct weak solutions to the 3D hypoviscous incompressible
elastodynamics with finite kinetic energy which was unknown in literatures. Our
result holds for fractional hypoviscosity $(-\Delta)^\theta$, where
$0\leq\theta<1$. The proof {consists of a convex integration scheme with new
building blocks of 2D intermittency and suitable temporal correctors, which are
motivated by} the inherent geometric structure of the viscoelastic equations.
