A multiple tube pulling apparatus for pulling, at one time, a plurality of stub-tubes from the tubesheet of a steam generator. Each tube gripping apparatus of the plurality is expanded into gripping arrangement by an axially retracted tapered rod. As the internal diameter of each stub-tube can vary, the amount of axial movement of each tapered rod to provide proper gripping engagement also varies. The present invention provides a single hydraulic cylinder for axially moving the plurality of tapered rods and includes spring members connecting each tapered rod to the hydraulic cylinder to accommodate the variations in axial movement of each rod necessary to obtain the proper gripping engagement for each stub tube. Further, a spring biased guide block maintains the gripping tubes on proper centers corresponding to the stub-tube centers and once the stub-tubes are removed from the tubesheet, the guide block pushes the stub-tubes off the tube gripping apparatus freeing the apparatus for another operation.