A tailpipe stone dumping vessel (1) for stone dumping through a fallpipe suspended from the vessel, comprising: • of a hull (1a), • a fallpipe section storage for storing fallpipe sections (2), • a tower (20) at least comprising fallpipe support means (40) for supporting the suspended fallpipe, said tower (20) being adapted for assembly and disassembly of the fallpipe by addition of a fallpipe section to the upper end of the suspended fallpipe or removal of a fallpipe section from the suspended fallpipe, respectively, • a tower gimbal structure (22) provided between the hull and the tower providing a pivotal mode for the tower (20) wherein the tower is pivotable about at least one pivot axis with respect to the hull so that the tower—and the fallpipe suspended there from—has in a plane associated with said at least one pivot axis an orientation essentially independent from sea-state induced vessel motions, • hoist means (31, 32, 33, 34) for lowering and raising the suspended fallpipe, • fallpipe section handling means (10-14, 31-34), adapted to—while the tower (20) is in its pivotal mode—advance a fall pipe section to the tower and to bring said fallpipe section in alignment with the uppermost end of the suspended fallpipe in order to assemble the fallpipe and adapted to—while the tower is in its pivotal mode—disconnect a fallpipe section from the uppermost end of the suspended fallpipe and advance it to the storage in order to disassemble the fallpipe.