  We prove the local in time existence of the classical solutions to the system
of equations of isothermal viscoelasticity with clamped boundary conditions. We
deal with a general form of viscous stress tensor $\mathcal{Z}(F,\dot F)$,
assuming a Korn-type condition on its derivative $D_{\dot F}\mathcal{Z}(F, \dot
F)$. This condition is compatible with the balance of angular momentum, frame
invariance and the Claussius-Duhem inequality. We give examples of linear and
nonlinear (in $\dot F$) tensors $\mathcal{Z}$ satisfying these required
conditions.
