A method and system for pneumatically conveying waste material through a conveying system which includes an input point for introducing waste material, at least one main conveying pipe section, at least one branch conveying pipe section, at least one separating device, and at least one pump unit for producing a pressure differential and air current within the operating system, whereby in a first phase, the main conveying pipe section functions as a material reservoir and in a second phase, the waste material is transferred to the separating device by the suction/pressure difference and/or conveying air flow produced by the pump device.