Abstract: This invention relates to a sheet stacking apparatus for stacking sheets into inclined trays moved past a sheet discharge zone. The trays each have first and second tray portions which are inclined to the horizontal and vertical, respectively, to enable a nested configuration. A pair of vertically extending stacking members are positioned adjacent to the sheet discharge zone to form an acute angle with the first tray portion of the receiving tray. The stacking member is pivotally mounted such that as a sheet enters the tray the kinetic energy of the sheet is converted to rotational kinetic energy. As the stacking member returns to its normal position, its rotational kinetic energy acts upon the topmost portion of the stack of sheets in the tray rather than upon a single top sheet. As a result the top sheet is not moved relative to the tray. As the stack height increases, the acute angle decreases to effect a stacking arrangement of the sheets' edges against the second tray portion.