One of the most important matters in keeping membrane structures in healthy condition is to maintain the proper tension distribution over the membrane. However, it is not easy to understand the real stress level in the membrane quantitatively after completion of the structures. Fluttering by strong wind or ponding caused by rain water may cause the severe damage of membrane structure itself and, therefore, it is very important to know magnitude of existing stress in constructed membrane structures for their maintenance and management. In this paper, a new method is proposed to measure membrane stresses in two different directions separately, where instead of measuring the membrane stresses directly, the natural frequencies of the membrane within fixed rectangular region resonated by sweep and white noise external excitation induced by sound.