The　problem　of　bending　of　uniformly　loaded　rectangular　plates　with　rest-on　edges,　i.　e.　Stoker＇s　problem,　is　discussed.　A　method　for　analyzing　the　problem　by　substituting　single-sided　line　supports　with　equally　spaced　single-sided　point　supports　and　turning　the　problem　into　solving　that　of　convex　quadratic　programming　has　been　developed.　With　the　help　of　a　Fourier　series,　Stoker＇s　problem　is　solved.　It　is　proved　that　the　contact　state　between　the　edges　of　plate　and　the　supports　is　stable.