Compared with the wide application of the membrane structures, the pretension measuring techniques for membrane structures have developed far more slowly. Further studies to search for a high-precision pretension measuring method which is reliable in theory and convenient for operation are not only necessary but also urgent. With the help of the finite element method, two important characteristics, the principles of "Stress Superposition" and "Stiffening Effect of Stress", are discovered and summarized in this article. The characteristics relate to the relationships between the pretensions of a stretched rectangular membrane with fixed boundaries around, the out-plane displacements at the central point of the membrane and the normal uniform loads applied on the membrane. Based on these two characteristics, a new method to measure the pretensions of membrane structures is proposed, which is celled "Numerical Measurement" in this paper. In the final part of the paper, a series of experiments are reported to validate the correctness of the method. The comparisons between the results of the method and those of the experiments are carefully made, which show that the two groups of results agree with each other very well. The results of mumerical simulations and experiments prove that our method is a reliable method, and the measuring results are of high precision.