In calculating piping systems components are taken into account by flexibility and stress intensification (SIF) factors. These factors, tabulated in codes, include many simplifications. Considering the component itself this leads to conservative results. Factors can yield wrong data referring to the elasticity of the whole system if the flexibility is computed in this way. Elbows play an enormous role in providing necessary elasticity to accommodate strains caused by temperature or accidental effects. For the elbow the pressureless bend is critical and the stiffness caused by the inside pressure can be ignored. However, this leads to mistakes in the calculation of the piping system elasticity and its reactions with the equipment. For this purpose results from papers are compared with own calculations and a lower limit for the stiffness of pipe elbows is given.