According to an embodiment, a sheet processing apparatus includes a first tray, a second tray, a first member, and a second member. The first member presses a first portion of a sheet toward the second tray when the sheet is moved from the first tray to the second tray located below the first tray. The second member is interlocked with the first member, and when the sheet is moved from the first tray to the second tray, presses a second portion of the sheet toward the second tray, the second portion being located downstream of the first portion in a transport direction of the sheet to the first tray.