In this paper is presented an approach for computing the first natural frequencies of parallel robots. This approach, based on the Rayleigh-Ritz approximation, aims at reducing the model dimension by decreasing the size of the matrices describing the robot mass and stiffness, saving computational time and avoiding inaccuracy due to ill-conditioning. Thus it can be used in the design procedure as well as in real-time control. Simulations are carried out on a PRRRP robot modelled in 3D and comparisons with FEA software are presented.