A folding umbrella and particularly one having multiple folds, includes a support frame incorporating a hybrid rib typically located intermediate a main rib and a rear or outermost rib. The hybrid rib is formed of multiple sections composed of first and second materials which respectively provide the desired structural strength to reduce inversions of the umbrella to an acceptable minimum and provide the hybrid rib with the desired resiliency and flexibility to return the hybrid rib to its original, unstressed shape and thereby prevent permanent damage to the hybrid rib as well as adjoining frame elements of the umbrella. The thicknesses of the multiple sections and the relative sizes of the sections also significantly contribute to the capability of the hybrid rib to achieve the desired objectives of a compact, small, folding umbrella of reduced weight, and the ability to prevent permanent damage to the frame due to inversion.