Measuring the in-plane mechanical stress in a taut membrane is challenging, especially if its material parameters are unknown or altered by the stress. Yet being able to measure the stress is of fundamental interest to basic research and practical applications that use soft membranes, from engineering to tissues. Here, we present a robust non-destructive technique to measure directly in-situ stress and strain in soft thin films without the need to calibrate material parameters. Our method relies on measuring the speed of elastic waves propagating in the film, which we validate with optical coherence tomography.