Structural models for foams having two‐dimensional cells with straight line segments and rounded corners are used to study the effect of gas volume fraction (φ) on small shearing deformations. A stress tensor expression is presented which is valid for all gas volume fractions between unity (dry foam) andφ=0.9069(hexagonally close‐packed cells). Two models are studied. In the first, the linear foam films are considered infinitesimally thin with all liquid in the foam confined to the Plateau borders. In the second model, the films have a finite thickness; the distribution of liquid between the Plateau borders and films varies with strain and is determined from an equal pressure drop requirement across all gas‐liquid interfaces. Identical results are obtained for the two models studied. The stress‐strain relation is a strong function of the gas volume fraction and, in general, the yield or minimum (negative) stress decreases with decreasing gas fraction. Unlike the dry foam model, initial cell orientation influences the stress‐strain relation significantly. For certain orientations and gas fractions, limit points and multiple solutions are observed, thus indicating possibilities of preferential cell orientation. Positive stresses are also observed in the stress‐strain cycle in many cases as the energy of the system passes through a maximum when the cells are deformed.