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

A local existence result for system of viscoelasticity with physical viscosity