Continuous deformable membrane mirrors are becoming more attractive for use in adaptive optics because they cause no diffraction in the reflected beam and ensure smooth and continuous phase variations across the mirrors. However, when such mirrors are used to correct a high-power incident wave front, the absorption in the coatings causes the temperature of the membrane to increase, thereby creating in-plane thermal stress due to the rigidly clamped boundaries. We present a technique to measure thermal stress in such nondeforming membrane structures. The directional stress and temperature effects are simultaneously measured and decoupled in micromachined membrane mirrors by using a group of three ion-implanted silicon resistors with different orientations. In stress measurements made with incident power, the sensors measure changes in compressive thermal stress to within 80-90 kPa.