Abstract: A two-stage method of expanding tubes into holes in tubesplates including walls of drums and headers especially in boilers using an elastomeric body which in a first stage is compressed axially in the tube and which expands radially to expand the tube beyond its elastic limit into close engagement with the hole wall. In a second stage a second elastomeric body of different dimensions is compressed axially to stress the tube and an annular zone of the tubeplate around the tube beyond their elastic limits. Problems of excessive extrusion of and damage to the elastomeric body where tolerances on tube or hole diameter produces excessive clearances are avoided even where high expansion forces are used.