A new molecular theory of tensile strength has been formulated for amorphous gum vulcanizates at temperatures well above the glass temperature and found to be in agreement with recent experimental data. It is shown that the stress on the rubber at break will consist of two parts, the normal kinetic theory stress on the network and the highly rate dependent stress held by the fully extended chains. The fraction of the chains in the fully extended state at the instant of break is greater for a lightly crosslinked rubber than for a highly vulcanized rubber under nonequilibrium test conditions. The theory allows the molecular weight of the freely orienting unit to be calculated. Reasonable values are obtained for EPR and SBR which lend support to the validity of the ideas involved. The kinetic-theory stress contributes the major portion of the stress at break in highly crosslinked amorphous gum rubbers. However, the stress at break for low degrees of crosslinking is largely the result of stresses in the most highly elongated chains.