This paper presents a numerical study on the effects of the width-to-thickness ratio, axial force ratio, and slenderness ratio on local buckling and strength deterioration of steel box columns subjected to cyclic loading. The maximum strength experienced during cyclic loading, and the strengths remaining after prescribed rotation angles are examined. The following observations are notable: 1) The maximum strength increases with a larger axial force ratio, but serious strength degradation is present due to local buckling; 2) The strength degradation is affected significantly by the width- to-thickness ratio, but the effect of the slenderness ratio is minor; 3) The width-to-thickness requirements stipulated in the present Japanese seismic design codes are not necessarily sufficient for columns sustain large cyclic loading up to 0.03rad in rotation.