Details of exciton dynamics in dye aggregates and supra-molecular complexes are substantially important for the functionality of molecular based opto-electronic devices. There are intensive theoretical studies of the multi-exciton dynamics in quantum dot structures but much less in molecular systems. Multiple excitons can be produced in molecular chains as well as two-dimensional and three-dimensional aggregates under an excitation of ultrafast strong laser pulse. According to the dipole arrangements of molecular chains, the coupled molecular chains are designed as H-H, H-J and J-H types of dipole configurations. In the scheme of density matrix theory, the dynamic processes of multiple excitons of different configurations are investigated by solving the quantum master equation through using the approximate dipole-dipole and expectation values of interest. The equations of motion for expectation values of interest governing the respective density operator are used to describe the temporal evolution of the multi-exciton states. It is found that the exciton energy band can be formed in the energy representation, and the multiple excitons are delocalized in the aggregates. The excitons represent different temporal evolutions excited by different resonant excitations. Compared with single-chain systems, double-chain systems have different degrees of blue shift or red shift due to interchain coupling. In the H-H type of aggregate, the electron population is lower if the double-molecule chain is simultaneously excited by the resonance frequency of a single molecule; the electron population increases to a certain extent if the frequency of the field is higher than the vibration frequency of a single molecule. The band width and the energy levels of the multiple excitons vary for different configurations of coupled molecular chains, and the wave packets show their own characters in these energetic levels. In the H-H type of aggregate, exciton state has priority to occupy the high-order energy level. The width of the exciton band of H-J type is significantly narrower than that of H single or H-H double chain configuration, because the Coulomb interaction of the inter-stranded dipole moment makes the whole energy low. In the J-H aggregates, the exciton states are more stable from the energy point of view, and the exciton energy band is wide because of the large Coulomb interaction. The energy of exciton state can be transferred via the interchain coupling, no matter which chain is excited. The transfer period directly correlates with the nearest interchain coupling.