The measurement of the elastic moduli of thin films on rigid supports presents many difficulties. The method described here consists in measuring the force required to press a plane-ended cylindrical plunger a given distance into a layer whose thickness is much less than the radius of the plunger. Mathematical analysis of this problem when the film is nearly incompressible but has low rigidity shows that this force is proportional to the depression and inversely proportional to the cube of the layer thickness. For thin layers of swollen gelatin this behaviour is experimentally confirmed, and values of the rigidity modulus are deduced.