The breaking strength, strain at break, and work to rupture of perfect fibers prepared with polymers of finite molecular weight are calculated by treating the perfect fiber as a stressed crystal undergoing a crystal‐melt phase transition. In this view, a tensile load destabilizes the crystal and depresses its melting point. When the load is sufficient to lower the melting temperature to the ambient condition the fiber melts—i.e., fails. The theoretical equations (extremely simple) are applied to several common polymer fibers. The maximum tensile strength of polyethylene, for example, is calculated to be 7 to 9 GPa, in good agreement with current experimental results.