A breakthrough buffer for a mechanical press (1) includes at least one buffer body (20) disposed between punch slide (2) and lower press frame (7) to cushion punch plate (3) during breakthrough of punch (4) through a workpiece, a timing regulator (40, 70, 90) connected to each buffer body for regulating timing of buffering during breakthrough, and a control system (60) to provide a command signal to this regulator to minimize noise or vibration occurring during the breakthrough. The control system includes a controller (63) which is responsive to the output of noise sensor (61) or vibration sensor (65) during breakthrough. The buffer body can include fluid driven buffer piston (22) in a buffer cylinder (21), with the buffer piston being associated with a guidepost (5). Alternatively, the buffer body can include piston (82) which contacts the guidepost and which is fluid driven (30, 81) in opposition to spring (83). The timing regulator can include an annular guide (46, 71) which is movable vertically by stepping motor (41) and worm gear drive (42, 44). A locking mechanism (73) can restrain trailing whirl of the guide. Alternatively, the timing regulator can include regulating piston (94) in regulating actuator (93), with fluid pressure on one side being controlled by proportional valve (91) responsive to the command signal, while fluid pressure on the other side is applied to each buffer piston.