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The elastic energy of a biaxially strained material depends on both the magnitude and the plane of the applied biaxial strain, and the elastic properties of the material. We employ continuum-elasticity theory (CET) to determine general analytic expressions for the strain tensor, the Poisson ratio, and the elastic energy for materials with cubic crystal symmetry exposed to biaxial strain in arbitrary planes. In application to thin homogeneously strained films on a substrate, these results enable us to estimate the role of elastic energy for any substrate orientation. When calculating the elastic response to biaxial strain in an arbitrary plane by numerical methods, our analytic results make it possible to set up these calculations in a much more efficient way. This is demonstrated by density-functional theory calculations of the Poisson ratio and elastic energy upon biaxial strain in several planes for the case of InAs. The results are in good agreement with those of CET, but show additional nonlinear contributions already at moderate biaxial strain.