Abstract: Passive intermodulation (PIM) products due to metallic contact nonlinearity at microwave frequencies can have severe effects on system performance. The principal mechanism and simplified model of metallic contact at microwave frequencies are discussed. The polynomial and matrix representations for arbitrary odd order PIM amplitudes are derived. General mathematical formulas regarding the third order and fifth order PIM power levels are given. As an example, prediction of the fifth order PIM power level with third order measured values is carried out by computer program. The calculated values are compared with experimental results, indicating that the predicted result practically agrees with the measured one.