A screen cylinder (125) used for screening cellulosic fibrous material pulp in the pulp and paper industry incorporates first (66) and second (67) downstream surfaces (16) having contoured slopes that form a funnel entrance of the grooves (13) at the screen cylinder slots (17). The contoured construction of the screen cylinder (125) effects greatly enhanced utility compared to conventional milled and discrete element screen cylinders, including substantially avoiding the Coanda effect .