AbstractAn extremal principle is formulated for the linear viscoelastic problem with general viscous kernel. This is an extension of the classical total potential energy principle of the linear elasticity. Then a discretized formulation in space and time is shown for frame structures, using finite element technique. Several numerical examples, for two different kinds of viscoelastic materials, testify the accuracy and reliability of the proposed method. The matrix conditioning indexes obtained are compared with those achieved by applying the least square method.