A blood processing system (2), includes a housing (4), to which a user control panel is mounted, having an access opening (47) therein. A cassette assembly (22), mounted to the housing for movement between a use position covering the access opening and a cassette-replacement position, includes a cassette holder and cassette (26) removably mounted to the holder. The cassette includes in part by tubing aligned with a through-hole (45) in the cassette. A door (34) is mounted to the housing for movement between a latched position, capturing the cassette between the panel and the door, and a released position. Independently-driven roller assemblies (46, 54, 72) pass part-way through the access opening to capture first tubing portions (44A, 52A, 68A) between the roller tracks (100, 102, 104) and the roller assemblies for peristaltic pumping of fluid. A number of movable pinch elements (48, 80, 90, 96) are extendable through the front panel to selectively pinch the tubing against the door and thus seal the tubing.