An apparatus for processing material in connection with a pneumatic material conveying system includes a waste container/separating device, into which material is configured to be conducted from a conveying pipe of the pneumatic material conveying system via an inlet aperture and which is configured to be connected to a partial vacuum generator. The apparatus further includes a press device/compactor device, which is arranged to act on the material (w) conducted into the waste container/separating device, via at least one aperture formed in the container, and that at least one wall that is transverse with respect to the input direction of the material is arranged in the container space of the waste container/separating device, which wall is configured to guide the material into the operating range in the container space of the compressor of the press device/compactor device.