When red blood cells are osmotically shrunk, opposing regions of the inner membrane surface touch each other in the dimple area. In normal red cells such a mechanical contact is undone by reswelling the cells. When the cells are treated with the SH reagents diamide or N-ethylmaleimide, or simply heated to temperatures between 42 and 48 degrees C such a mechanical contact can be made permanent by a process termed 'membrane cross bonding'. Cross bonding also occurred when the cells were treated before mechanical contact was established. The bridge between the two cross-bonded membrane regions may be assumed to be formed by membrane skeletal material. Membrane bridges become visible microscopically when the cells are swollen. These bridges are strong enough to resist the membrane tensions occurring at osmotic lysis. Bridged red cells can be a useful tool in rheology, since they are deformable but cannot adapt to shear flows by membrane tank treading.