The study deals with the computation of the linear vibrations of prestress elastic structures. The originality of the proposed approach is based on a Proper Orthogonal Decomposition (POD) associated with a modal projection-based Reduced Order Model (ROM) to evaluate the natural frequencies of an elastic structure in function of a static pressure load parameter. It is shown that a finite number of POD modes combined with linear prestress eigenmodes are able to evaluate efficiently the frequencies function of the evolution parameter. The generated reduced order model can be used in future works on parametric studies, sensitivity analyses, optimization procedure or feedback control loops systems.