Abstract: The focus cabin of the FAST (Five-hundred meter Aperture Spherical radio Telescope) is supported and driven by six parallel flexible steel cables, so that it is suspended in the air and traces a spherical focal surface.As a result, the orientation of the focus cabin is adaptive to the variable spatial position of the focus cabin.The adaptation nevertheless raises the risk of overturning of the focus cabin during its motion.In this paper we first theoretically analyze the mechanics of overturning of the focus cabin and present verification of the analysis through experiments on a 3m scaled model of the FAST focus cabin-cable system.We then establish an object function of optimization of the critical tilt of overturning of the focus cabin by taking the static-equilibrium equations and the limits on cable tensions/cabin orientations as the constraint conditions.We employ the Newton Iteration Method to obtain optimal solutions of the critical tilts using the function.We have also evaluated and tested the effect of the location of the center of gravity (COG) of the focus cabin on the critical tilts.Our test results show accurate consistency with our theoretical analysis.We finally present the calculation results of the critical tilts of the actual focus cabin at all its accessible locations on the focal surface.The results show that a cabin tilt under a normal circumstance is much less than the critical tilt of overturning of the focus cabin.This means the focus cabin is normally safe.