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Equations for calculating the shear modulus of non-isotropic, open cell foams in the plane perpendicular to the rise direction and in a plane parallel to the rise direction are derived using an elongated Kelvin foam model. This Kelvin foam model is more general than that employed by previous authors as the size and shape of the unit cell are defined by specifying three independent cell dimensions. The equations for the shear compliances are derived as a function of three unit cell dimensions and the section properties of the cell edges. From the compliance equations, the shear modulus equations are obtained and written as a function of the relative density and two unit cell shape parameters. The dependence of the two shear moduli on the relative density and the two shape parameters is demonstrated.