This study presents an ordinary state-based peridynamic (PD) “truss” element for modeling viscoelastic structures under mechanical and thermal loads. The truss element enables the peridynamic interactions among the finite element nodes. The behavior of the viscous material is modeled in terms of Prony series. The constitutive constants are the same as those necessary in the classical history-integral model, and they are also readily available from relaxation tests. Unlike the traditional finite element connectivity, the PD interactions result in a sparsely populated global system stiffness matrix. The peridynamic truss element predictions are verified against finite element analysis with traditional elements. The numerical results concern the viscoelastic behavior of isotropic plates under different boundary conditions when subjected to mechanical and thermal loads.