The present invention relates to a tissue infiltration device (1) for samples (34) contained in cassettes (5). The tissue infiltration device (1) comprises at least two liquid containers (7, 11a-11d, 13, 15) and a transport apparatus (6). A liquid (12, 14, 16) having a property that can be predetermined can be filled into a liquid container (7, 11a-11d, 13, 15). A plurality of cassettes (5) can be held by a transport device (4). Using the transport apparatus (6), a transport device (4) can be brought to a liquid container (7, 11a-11d, 13, 15) and/or moved away from a liquid container (7, 11a-11d, 13, 15). A sequence of operations (8) can be prescribed in which a transport device (4) runs through the liquid containers (7, 11a-11d, 13, 15) of the tissue infiltration device (1). So that an accelerated or priority processing of a transport device (4) is possible using the tissue infiltration device (1), but without using an additional liquid container (7, 11a-11d, 13, 15) provided only for this purpose, it is provided that at least two transport devices (4) can be brought into a liquid container (7, 11a-11d, 13, 15) above and/or next to one another, wherein said transport devices can have different dwell times in the liquid container (7, 11a-11d, 13, 15).