In this study, we investigate primary buckling modes and stresses of a Kelvin open-cell foam under uniaxial compression in [001], [011], and [111] directions. For this purpose, a homogenization framework (Ohno et al., 2002 ; Okumura et al., 2004) is employed to analyze the macroscopic instability as well as the microscopic bifurcation depending on periodic unit length. In this analysis, ligaments of the Kelvin open-cell foam are assumed to be made of an isotropic elastic material and to have a nonuniform cross-section described by two geometric parameters. It is shown that the buckling behavior is anisotropic in the three directions of uniaxial compression ; the primary buckling modes in the [001] and [011] compressions are caused by long wavelength bifurcation accompanying the onset of macroscopic instability, while that in the [111] compression is done by short wavelength bifurcation. However, their primary buckling stresses are nearly identical, and moreover are in reasonably good agreement with an analytical prediction combined with experiments. It is also shown that the non-uniformity of the cross-sectional area plays a dominant role in the buckling behavior.