Thick matter pump and method for conveying thick matter

A thick matter pump having a conveying chamber, which extends along a closed path from an inlet opening, via an outlet opening, back to the inlet opening, so that the conveying chamber forms a first connecting path and a second connecting path between the inlet opening and the outlet opening, having a first piston for performing a conveying movement along the first connecting path of the conveying chamber, so that with the conveying movement thick matter is conveyed from the conveying chamber through the outlet opening, and thick matter is introduced into the conveying chamber through the inlet opening, and having a shut-off element in the conveying chamber which shuts off the second connecting path in a first state, and opens up the second connecting path in a second state, in order to allow a movement of the first piston along the second connecting path, wherein a wall shell delimiting the conveying chamber is attached to the first piston, which wall shell extends over the entire length of the conveying chamber and is moved together with the first piston.