The simple idea that a strain applied to a thin polycrystalline metal film bonded to a rigid substrate sets up gradients of plastic shear over distancos determined by film thickness and grain radius has made it possible to predict the yield stress of thin films as a function of film thickness, grain size and internal strain. Compatibility of deformation between differently deforming substrate and film materials and between differently oriented grains can be achieved by the formation of' geometrically necessary' dislocation arrays, the density of which depends on the gradients of shear strain and can be calculated. The yield stress of thin films can be accounted for in terms of these geometrically necessary dislocations and the general results of work-hardening theories relating yield stress to dislocation density. Values of yield stress have been calculated for a given thermal strain for lead films deposited by a variety of techniques, so giving different dependences of grain size on film thickness. Using these values a limiting film thickness which can sustain the thermal strain without plastic deformation was predicted for each case. The predicted limiting film thicknesses are in excellent agreement with the ones determined experimentally by Murakami (1978, 1979 a) using X-ray diffraction techniques. © 1979 Taylor & Francis Group, LLC.