A manufacturer of systems which filter a mixed inlet gas stream and produce virtually pure hydrogen required structural analysis. Their process imposes an extremely high number of pressure cycles on the vessels containing the filtration medium. We were asked to develop simple methods for determining stresses in the heads, nozzles, support features and other structures. These stresses were found as functions of various dimensional relationships and of the stress in the cylindrical shell. From this information, it was feasible to determine the fatigue life of the filter vessels without extensive detailed analysis of each vessel.