NOVELTY - Rubber composition comprises (a) at least one rubber compound and (b) at least one radical initiator, where the component (a) is radically crosslinkable and contains at least 50 phr (parts by weight per 100 parts by weight of rubber) of completely or partially hydrogenated polyisoprene having a melt viscosity of less than 105 Pas at 38 degrees C.    USE - The rubber composition is useful for preparing: elastomers; and molded bodies, which are gaskets, impregnating-, coating-, membrane- or adhesive-composition preferably for hoses, valves, pumps, filters, humidifiers, reformers, storage jars, vibration dampers and acoustically active components. The rubber composition is useful as: a coating for woven and non-woven fabrics, electromagnetic shield, tires, brake seals, brake parts, axle boots, bellows, floor coverings, profiles, membranes or gas diffusion layers for fuel cells. The molded body is useful in fuel cell, and/or production-, transport-, processing technique- and packaging-sectors of food or medicinal products (all claimed).    ADVANTAGE - The composition: can be prepared, handled and processed easily; has good mechanical property, improved stability including tensile strength and elongation and tear strength; is insensitive; allows for the addition of various additives such as fillers without imparing the crosslinking reaction; and does not contain plasticizers and thus preventing the unwanted side reactions and side effects associated with the use of the plasticizers. The molded bodies, prepared from the composition, have excellent mechanical properties, and low hardness.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) a method for preparing the rubber composition, comprising mixing the components (a) and (b) together and optionally homogenizing;    (2) a method for preparing molded bodies, comprising radically crosslinking the composition optionally under high temperature; and    (3) a molded body obtained by the above method.