In this study, a three‐mode approximate theory governing axisymmetric motions in transversely isotropic rods is developed. The development of this approximate theory follows closely the method adopted by Mindlin and McNiven when they developed a three‐mode theory for isotropic rods. There is, however, one significant departure. After the generalized displacements and generalized strains are defined, the equilibrium and constitutive equations and the kinematic relations are derived using a variational theorem due to Hu and Washizu. The approximate theory is analyzed numerically for two transversely isotropic materials, and spectral lines derived from the theory are compared with those from the exact three‐dimensional theory.