This paper investigates the dynamic response problem of an orthotropic rectangular membrane structure excited by the heavy rainfall. Firstly, a determined model is proposed to express the load of heavy rainfall imposed on the membrane structure. Then, the geometrically nonlinear governing motion equations of the membrane structure are established based on the von Kármán’s theory, and solved by the perturbation method. Consequently, the approximated analytical solution of displacement can be obtained. Secondly, the experimental study of this dynamic response problem is carried out. The theoretical model is validated by the experimental data based on the developed artificial simulated rainfall impact system. Moreover, the effects of adding weight from the accumulated rain on structural characteristics are analyzed. Additionally, the parameter discussions varying with rainfall intensity, material properties, pre-tension, structural size, and inclined angle are made in detail. This work provides a reliable theoretical model and experimental system to study the dynamic response problem of membrane structures excited by heavy rainfall and the guidance for the dynamic design, construction and maintenance of membrane structures in practical engineering as well.