We have developed a high-throughput technique, SHAPE-Seq, that can simultaneously measure quantitative, single nucleotide-resolution secondary and tertiary structural information for hundreds of RNA molecules of arbitrary sequence. SHAPE-Seq combines selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) chemistry with multiplexed paired-end deep sequencing of primer extension products. This generates millions of sequencing reads, which are then analyzed using a fully automated data analysis pipeline, based on a rigorous maximum likelihood model of the SHAPE-Seq experiment. We demonstrate the ability of SHAPE-Seq to accurately infer secondary and tertiary structural information, detect subtle conformational changes due to single nucleotide point mutations, and simultaneously measure the structures of a complex pool of different RNA molecules. SHAPE-Seq thus represents a powerful step toward making the study of RNA secondary and tertiary structures high throughput and accessible to a wide array of scientific pursuits, from fundamental biological investigations to engineering RNA for synthetic biological systems.