Improper aligning of shafts through couplings often leads to severe vibration problems in many rotating machines. The rotor-bearing system is modelled using higher order finite elements by considering deflection, slope, shear force, bending moment with eight degrees of freedom per node. The reaction forces, moments developed due to flexible coupling misalignment are derived and introduced in the model. The imbalance response in two harmonics is evaluated. The increase in harmonics with misalignment can easily be modelled by using FEM analysis. The location of the coupling with respect to the bending mode shape has a strong influence on the vibrations. © 1995 Academic Press. All rights reserved.