The effects of damping on the behaviour of simple and combination resonances of simply-supported rectangular plates subjected to non-uniform in-plane periodic loading are studied. Finite element formulation is applied to obtain the equilibrium equation for the plate. The relations for the boundaries of parametric instability regions are obtained by using the method of multiple scales. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. For nearly uniform loading, the combination resonance zones are very small in width and may disappear in the presence of slight damping. The effects of damping show that there is a finite critical value of the dynamic load factor for each zone below which the plate cannot become dynamically unstable. It is also shown that the effects of damping on the combination resonances may be destabilizing under certain conditions.