Method for conveying and handling waste material in the channel section of a pneumatic wastes conveying system, in which method solid waste material or recycleable material fed into a conveying pipe is conveyed in the conveying pipe of the pneumatic pipe transport system for material along with the transporting air flow to the delivery end of the material conveying system, where the material is separated from the transporting air. In the method the material is acted upon in the conveying pipe by stopping the speed of movement of the material being conveyed in the conveying pipe by means of a stopper arranged between the separating device of the delivery end and the material being handled, or against the stopper at, or in the proximity of, the delivery end of the material conveying system and by bringing about in the channel space of the conveying pipe volumetric compression in at least a part of the material being conveyed by means of the stopper arranged between the separating device of the delivery end and the material being handled, or against the stopper, by means of a pressure difference acting on the different sides of the material being handled, such as by the combined effect of suction and replacement air, before transportation of the material onwards in the conveying pipe into a container of the separating device arranged at the delivery end of the pneumatic transport system for wastes.