The synchronization of paper feeding to the offset printing machine drums from feeding pile is carefully design. The suction head is responsible to attract the paper from the pile by the power of vacuum. The vacuum pressure at the suction head should has the strength to hold the paper and at constant rate by the effect of the in line suction damper that reduce the vacuum pump pressure pulsation. In this paper, an unsteady mathematical model for the in line suction damper has been developed. A series of in line suction dampers with constant volume and different chamber matrix construction has been introduced. The effect of in line suction damper chambers matrix on the dynamic performance of rough vacuum system has been studied at different inlet vacuum pressure oscillations. Up to our knowledge there is no analytical model to explicitly characterize this phenomenon. The unsteady paper pickup force produced from different damper construction is introduced. It has been concluded that both flow path of 9 chamber design are the more useful design than the rest of damper design and is a good choice as an inline suction line vacuum damper in the paper feeding mechanism of printing machine.