In the autofrettage process, a thick-walled workpiece (2) to undergo autofrettage is positioned in an autofrettage apparatus (1). The interior space (5) of the workpiece (2) is filled with a fluid and closed so as to be pressure-tight. The volume available to the fluid in the interior space (5) of the workpiece (2) is reduced by a displacement piston (19) which is moved into the interior space (5) of the workpiece (2) through a displacement piston opening (6) of the workpiece (2). The pressure is therefore generated in the interior space (5) of the workpiece (2).