On the basis of a computer program developed, optimization of the main parameters of the composition and molecular structure of a three-dimensionally cross-linked elastomer composite for the fracture energy in uniaxial tension is investigated. By a numerical simulation — varying the structural parameters and molecular structure — the maximum value of fracture energy is found (the direct problem); for a given value of fracture energy, the required parameters of the composition are determined (the inverse problem). The solutions to the problems considered can be used in the engineering practice in creating frost-resistant moisture-proof coatings and expansion joints of asphalt highways.