Interaction of cavity modes with an exciton in a meso-cavity (the structure supporting several cavity modes separated by an energy interval comparable to Rabi-splitting of an exciton and cavity modes) has been analyzed using a quantum-mechanical approach. Simultaneous interaction of an exciton and several cavity modes results in few novel effects such as ladder-like increase of the exciton population in the system, quantum beating and non-monotonic dependence of the ground polariton state in the system on the pumping.