We propose a simple new method for measuring the surface shear elasticity modulus (mu) together with the dilatational modulus (K) of gel-like protein layers on an air/water boundary. The stress response to compression/expansion of the interface in a Langmuir trough is measured at two different orientations of a Wilhelmy plate, collateral and perpendicular to the movable barrier in the trough. The interfacial tension is a tensorial quantity, whence the measured values depend on the direction of the length along which the stress acts. The fact that the deformation in the trough is uniaxial, i.e., a combination of dilatation and shear, is used to determine the respective two elastic moduli (K,mu). The experiment demonstrates that adsorbed layers of beta-lactoglobulin (BLG), when subjected to small deformations, exhibit a predominantly elastic rheological behavior. This proves the existence of the two-dimensional gel, as a result from partial denaturation and unfolding accompanied with entanglement of the protein molecules on the interface. Layers of this kind exhibit finite shear elasticity (mu not equal 0). Data are reported for systems containing BLG at different concentrations, and for mixtures including low molecular weight nonionic surfactant Tween 20. The elastic moduli are found to increase with rising protein content (at relatively higher concentrations), which is perhaps due to reinforcement of the gel-like structure. It is proved that in all cases the presence of Tween 20 brings about a complete fluidization of the adsorbed layer, in the sense that the shear elasticity disappears and the respective modulus (mu) becomes equal to zero. The frequency dependence of the elastic moduli is discussed in view of possible exchange of protein molecules from the interface with the bulk or with the adjacent subsurface layers.