Explicit expressions are derived for the collapse and elastic post-buckling of simply supported, geometrically imperfect plates with stress-free edges. For the purposes of design, such plates can be taken as representative of the stiffened compression elements of thin-walled structural sections. Different generalized geometric imperfection parameters are studied and the effects compared to established test data obtained from cold-formed steel sections subjected to either bending or compression. For these sections a suitable and completely general parameter describing the imperfection amplitude, e\d0t, of a plate of thickness t is shown to be e\d0=0.2σ\dy/σ\Dcr\N in which σ\dy is the yield strength of the plate material; σ\Dcr\N is the theoretical local buckling stress of the equivalent ideal plate and is a direct function of its width to thickness ratio. This parameter is recommended for the design of cold-formed steel sections against local buckling.