The existence of the many formulas and design aids that are utilized for the design of mechanical joints show that a great variety of components can be held together by using rivets, bolts, welds, and adhesives. One of the more difficult topics addressed today involves the mechanism of interaction between pipes and the pipe clamps. One of the special problems in the design of pipe clamps is concerned with determining clamp stiffness that depends on a number of component stiffnesses arranged in series. This chapter includes a very wide selection of pipe-line supports, clamps, split hubs, and similar connections. The majority of pipe clamps are of the yoke beam or ring type involving highly nonlinear distribution of interface pressure and the resulting hoop stresses. The forces developed in the pipe clamps are caused by the combined effect of external loads, internal systems pressure, and thermal gradients. The stiffness of the pipe branches and the supports can be extremely important.