Using a symmetry adapted density matrix renormalization group (DMRG) formulation, we have calculated various optical spectra, including linear absorption, electroabsorption, third-harmonic generation, and two-photon absorption, for a series of linear polyene molecules (up to 40 carbon sites) modeled by an extended Hubbard-Peierls Hamiltonian within the intermediate correlation regime. The theoretical two-photon absorption spectrum for trans-octatetraene is in good agreement with experiment. By comparing the experimental linear absorption spectra and theoretical higher A(g) state energies, it is suggested that the so-called cis-band actually corresponds to the threshold of the mA(g) band.