Abstract. -We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 ± 0.4 pJ·m −1 ) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, µ = 38±3 nN·m −1 . The foam effective rigidity is predicted to be 35 ± 3 nN · m −1 , which agrees with the value 37.obtained in an independent mechanical measurement.Introduction. -A liquid foam, made of polyhedral gas bubbles separated by thin liquid walls forming a connected network [1], is a mixture of two fluids. It has nevertheless a solidlike elasticity, characterised by a shear modulus µ, proportional to the surface tension of the walls [2,3]. In fact, shearing a foam modifies the total length of the walls, thus the foam energy. The value of µ can be determined in numerical simulations [4,5,6]; however, it is still an open problem to predict analytically its value for a real foam, which has a finite fluid fraction and an inherent disorder due to its distribution of bubble sizes.Here, we compare two experimental measurements of µ. First, by global mechanical measurements on the scale of the whole foam, described in terms of elasticity of continuous media. Second, and simultaneously, by detailed imaging of the diphasic foam structure, on the local level of a few bubbles: this suggests to use two-dimensional (2D) foams. In the literature, 2D soap froths have been sheared in Couette geometry, either as bubble rafts [7,8,9] or confined in Hele-Shaw cells between two parallel plates of glass [10].We investigate the elasticity of a real 2D system: a "Langmuir foam" [11]. A monomolecular layer of amphiphilic molecules deposited at the surface of water ("Langmuir monolayer") exhibits a first order transition between a 2D gas phase and a denser 2D liquid (also called