Parametric model reduction addresses a broad class of problems in which the equations governing the dynamic behaviour of a structure depend on a set of parameters, such as material properties, geometry, initial conditions, boundary conditions and loads. In these cases, the primary objective is to generate a parametric reduced model that accurately approximates the original full-order system with high fidelity over a given range of parameters. Paper [1] provides a review of the main parametric model reduction methods for dynamical systems. The application of Proper Orthogonal Decomposition (POD) techniques to obtain reduced-order models of linear dynamic structural systems is described in [2], where the authors analyse the 39-story Pirelli Tower in Milan, Italy. Applications of POD to nonlinear systems are presented in [3]. For structures with constitutive nonlinearities, the internal forces in the equations of motion depend nonlinearly on the displacement. Unlike the linear case, these forces must be evaluated for the full system at each time step. This drawback makes model order reduction particularly challenging and highlights the need for numerical techniques capable of keeping computation costs within reasonable limits, as suggested in [4]. This paper presents the first results of applying the POD method to the nonlinear dynamic analysis of masonry structures. The numerical investigations focus on a simple masonry structure and aim to assess the performance of the POD technique by modelling the masonry material as a nonlinear elastic material [5]. After a brief description of the integration scheme adopted to solve the nonlinear equations of motion of both the full and reduced-order models, the quality of the POD solutions is assessed through comparison with the responses of the masonry structure subjected to several real earthquake records.