The electronic structure of the allyl radical C3H5 and the polyene radicals C5H7, C7H9, C9H11, and C11H13 have been calculated using the linear combination of Gaussian-type orbitals-local spin density method. In contrast to the results obtained using the Hartree-Fock model, which show large errors, the geometries are in excellent agreement with multiconfiguration self-consistent-field calculations and with experiment. LSD yields a C2-upsilon symmetry for the allyl radical, while the polyenes C5H7 to C11H13 have C-C bonds alternating between single and double bonds. The harmonic vibrational frequencies were calculated for the allyl radical and C5H7 (the 1,4-pentadienyl radical). The unscaled vibrational frequencies calculated for the allyl radical are in excellent agreement with experiment.