A dynamic approximate theory capable of predicting high‐frequency behavior of cylindrical thermoelastic bars is developed using a new theory. The cross section of the bar has an arbitrary shape and contains an arbitrary number of holes. The approximate theory is valid for all of the deformation modes such as flexural, longitudinal, torsional, etc. The use of the new method permits one to eliminate any inconsistency which may occur between lateral boundary conditions and the distributions of displacements or temperature assumed over the cross section of the bar. Accordingly, the method enables one to correctly describe the reflections of the waves propagating along the bar. This, in turn, makes the dispersive characteristics of waves in bars predicted by the approximate theory agree with those obtained from the exact theory without having to introduce any matching coefficients into the approximate theory.