With the dynamic element method (DEM), results more accurate than with the conventional finite element method (FEM) are obtained with the same number of degrees of freedom. This is due to the introduction of shape functions of polynomial type, introducing frequency dependence into the mass matrix expressions. It is demonstrated how this affects free vibration analysis, including the solution of nonlinear eigenvalue problems. Various numerical techniques for solving these polynomial problems are discussed. The polynomial matrix formulations for stiffness and mass matrices are given for a beam, a bar and a cable element. Numerical examples demonstrate how the DEM can be implemented for modelling of frame type structures and its efficiency is compared to that of the conventional FEM