The spin-restricted formulas for the analytical gradients of the second-order IC Moller-Plesset perturbation (MP2) energy are presented within the framework of ab initio crystal orbital theory of infinite one-dimensional lattices (polymers). The coupled perturbed Hartree-Fock equation for polymers is solved iteratively using the atomic-orbital-based algorithms. The MP2 energy and its gradient contributions are evaluated by the disk-based algorithms with the aid of the two-particle density matrix. The analytical-gradient method at the MP2 level, as well as the analytical first- and second-derivative methods at the Hartree-Fock (HF) level, is applied to calculate the equilibrium structures and harmonic vibrational frequencies of all-trans polyacetylene. The deviations of the calculated frequencies from the observed ones for the in-phase C=C stretching modes are reduced by about 70% on going from HF/6-31G to MP2/6-31G theory.