A tube bundle device useful in heat exchangers, condensers and other devices which has a number of tube support cages placed at extended locations along the length of the tubes. After the initial construction of the bundle in which the tubes are inserted into the support cages the tube bundle is stiffened by inserting sets of tube stakes between the tube support cages, preferably at the midpoint of the tube span between the cages. The tubes are supported by rods or bars in each tube lane at the tube support cage locations and the rods in each cage are rotated axially with respect to the rods in the next adjacent cage; in a similar manner, the stakes in each set are rotated axially with respect to the stakes in the next axially adjacent set.