A finite element method is presented for studying natural vibrations and waves in pretwisted rods. The analysis is based on three-dimensional elasticity using a coordinate system that rotates with the cross-section. Finite element modeling occurs over the cross-section, so that arbitrary geometry and inhomogeneous, anisotropic material properties can be accommodated. The variationally derived equations of motions are partial differential equations in terms of the axial coordinate and time. Specifying the solution as a harmonic wave form leads to an algebraic eigensystem from which the natural frequencies and corresponding modal patterns of vibration can be extracted. Because of the pretwist, the harmonic wave forms for extension/torsion waves and flexural waves must be expressed separately. Two examples, a homogeneous, isotropic bar and a two-layer ±30° angle-ply composite bar where both have the same rectangular cross-sectional shape, are given to illustrate the method of analysis and the physical behavior of these two members.