The nonlinear optical absorption spectrum of conjugated polymers is theoretically studied in the Pariser-Parr-Pople model. The method of configuration interaction among single and double excitations is employed for relatively long chains up to 40 sites with the cyclic boundary condition. Calculated spectra in the case of moderate electron-electron interactions are characterized by two groups of peaks : low energy peaks mainly due to excitonic states and high energy peaks with main contributions from biexcitonic states. The latter peaks are much stronger than the former. We examine also how the spectrum depends on the bond alternation and the interaction strength.