A modal procedure for the computation of the unbalance response of rotors modelled as systems with many degrees of freedom (possibly by using the finite element method) is suggested. If damping is neglected, the procedure is quite similar to that usually followed for a non-rotating structure, the only difference being the possibility of obtaining also modes with negative modal masses which cannot in general be neglected. Following a similar procedure damped systems can be also studied; if the distribution of damping is not "proportional", an iterative approach that is cost-effective from the computational point of view is suggested both for natural and non-natural systems. The modal procedure is extended also to the case of non-isotropic machines with a non-symmetric stator or non-symmetric rotor. A computational procedure which can be used for the computation of the "backbone" and the stable branches of the response of non-linear systems is shown. An example of application to a rotor with many degrees of freedom is also reported.