The applicability and evaluation of a new self-starting, unconditionally stable, implicit methodology of computation for the dynamics of structures is described. The methodology offers different perspectives and architecture for structural dynamics compared with the tranditional (widely advocated and commonly used) time integration methods. It is based on velocity representations and architecture and uses finite elements as the principal analysis tool for structural dynamic modeling/analysis. In particular, the dynamics of beam-type flexural models are considered, and comparative results validate and support the proposed use of the self-starting methodology of computation for the dynamics of linear/nonlinear structures. The overall effectiveness and elegance strongly support its use in most existing commercial codes.