A cassette processing apparatus has a plurality of stack units for holding respective cassettes in an array, and a tilting mechanism for tilting the cassettes held by the respective stack units at respective different angles depending on the types of the cassettes. The tilting mechanism has a rotatable shaft connected to a rotary actuator, and a plurality of eccentric cams held in respective angular positions by the rotatable shaft to adjust the angles at which the stack units are tilted thereby to set angles at which the cassettes are titled.