The low‐frequency dynamics (<20 meV) of pure and sodium‐doped trans polyacetylene are investigated using a combination of incoherent neutron scattering spectroscopy and molecular dynamics simulations. The simulations are performed using a molecular mechanics potential function and including explicitly the three‐dimensional crystal environments of the molecules. Both the experiments and the simulations indicate that doping results in a marked change in the vibrational density of states of the polyene chains in the direction perpendicular to the chain axes, a broad minimum appearing at ∼16 meV. This spectral region is dominated by intramolecular torsional displacements. The results also suggest that the mean‐square displacements of the polyacetylene atoms become more isotropic on doping. The contributions of various rigid‐body motions to the simulation‐derived mean‐square displacements and vibrations are described.