A membrane deflection technique has been developed to measure the isotropic residual stress in biaxially-constrained coatings. The technique has been demonstrated on various materials, including polyimide, latex rubber and photoresist coatings. Stress values obtained from membrane deflection compared well with results obtained from time-averaged vibrational holographic interferometry except for values obtained from samples where rigidity effects were found to be important. A criterion based on the thickness, rigidity, stress and sample radius is also discussed, establishing the applicability of the technique to samples of low rigidity.