To discover new materials, high-throughput screening (HTS) with machine learning (ML) requires universally available descriptors that can accurately predict the desired properties. For elastomers, experimental and simulation data in current descriptors may not be available for all candidates of interest, hindering elastomer discovery through HTS. To address this challenge, we introduce structure-based multilevel (SM) descriptors of elastomers derived solely from molecular structure that is universally available. Our SM descriptors are hierarchically organized to capture both local soft and hard segment structures as well as the global structures of elastomers. With the SM-Morgan Fingerprint (SM-MF) descriptor, one of our SM descriptors, a machine learning model accurately predicts elastomer toughness with a remarkable accuracy of 0.91. Furthermore, an HTS pipeline is established to swiftly screen elastomers with targeted toughness. We also demonstrate the generality and applicability of SM descriptors by using them to construct HTS pipelines for screening elastomers with a targeted critical strain or Young's modulus. The user-friendliness and low computational cost of SM descriptors make them a promising tool to significantly enhance HTS in the search for novel materials.