  We consider the linear system of viscoelasticity with the homogeneous
Dirichlet boundary condition. First we prove a Carleman estimate with boundary
values of solutions of viscoelasticity system. Since a solution $u$ under
consideration is not assumed to have compact support, in the decoupling of the
Lam\'e operator by introducing div $u$ and rot $u$, we have no boundary
condition for them, so that we have to carry out arguments by a
pseudodifferential operator. Second we apply the Carleman estimate to an
inverse source problem of determining a spatially varying factor of the
external source in the linear viscoelastitiy by extra Neumann data on the
lateral subboundary over a sufficiently long time interval and establish the
stability estimate.
