AbstractAn intrinsic beam formulation has recently appeared (AIAA J. 2003; 41(6):1131–1137), which presents the three‐dimensional equations of motion governing spatial and temporal changes in a one‐dimensional continua's curvature, strain, rectilinear velocity, and angular velocity. The formulation would suggest several computational advantages over more‐traditional displacement‐based continua approaches: low‐order interpolation functions can describe generally curved and twisted continua configurations; inter‐element displacements, slopes, strains, and curvatures can be matched; and finite rotational variables and their complexities are absent. Here, we present a completed intrinsic continua finite element development and critical analysis, which follows from an earlier preliminary treatment as applied to carbon nanotubes (Int. J. Solids Struct. 2007; 44:874–894). Modeling of nodal displacements and rotations are included. Explicit time stepping, with desired high‐frequency damping, is accomplished using an implementation of the generalized‐α method. Zero‐energy modes inherent in the formulation are also identified and rectified. Finally, we document very good agreement between results predicted with the intrinsic continua finite element simulator and results generated using more‐traditional finite element simulations. Copyright © 2009 John Wiley & Sons, Ltd.