We report on spatially resolved measurements of the mechanical stress in drying polymer films. The technique is based on the deflection of a flexible membrane serving as the substrate. Assuming that the lateral tension of the membrane is the main source of its resistance to deformation, one can show that the local surface stress σf (x,y) is proportional to the vertical displacement of the membrane uz(x,y). The membrane distortion was determined by optical means. Measurements taken on drying latex dispersions revealed a maximum of film stress at the rim. The heterogeneous stress distribution often persisted after the film had become dry.