The elasticity of open and closed thin foam films is analyzed. The elasticity modulus of a closed film is shown to be additive with respect to contributions from Gibbs elasticity and disjoining pressure. A detailed expression for the film elasticity modulus explains the pronounced maxima of foaminess and foam stability near the critical micelle concentration observed earlier in many experiments. A theory of transversal elasticity of thin foam films is formulated under conditions excluding the action of Gibbs elasticity. Near the critical micelle concentration, the theory predicts maxima of the transversal elasticity modulus and of the films thickness as functions of concentration at a given disjoining pressure. The prediction has been verified experimentally by measuring the film thickness in equilibrium foam as a function of height.