The two-photon capture cross sections for pyrene and 3,4-benzpyrene are calculated using SCF-CI pi-electronic wavefunctions and the theory of Goeppert-Mayer. The cross section is shown to be dependent on the product of the photon flux and a constant, S, which may be calculated from suitable matrix elements and the line shape function. For randomly oriented molecules and polarized light the calculated values of δ for pyrene and 3,4-benzpyrene are, respectively, 260×10-51 and 1500×10-51 cm4·sec atom-1 photon-1. These are to be compared with the experimental values of, respectively, 1×1051 and 50×1051 cm4·sec atom-1- photon-1. The effect of molecular symmetry on the two-photon absorption of polarized light is illustrated for molecules of D2h symmetry. For a two-photon transition to a B1g, state, the maximum probability is shown to lie approximately 45° between the x and y axes of the molecule which are the axes of maximum probability for one-photon absorption.