Prediction of RNA structure from nucleotide sequence remains an unsolved grand challenge of biochemistry and requires distinct concepts from protein structure prediction. Despite extensive algorithmic development in recent years, modeling of noncanonical base pairs of new RNA structural motifs has not been achieved in blind challenges. We report a stepwise Monte Carlo (SWM) method with a unique add-and-delete move set that enables predictions of noncanonical base pairs of complex RNA structures. A benchmark of 82 diverse motifs establishes the method's general ability to recover noncanonical pairs ab initio, including multistrand motifs that have been refractory to prior approaches. In a blind challenge, SWM models predicted nucleotide-resolution chemical mapping and compensatory mutagenesis experiments for three in vitro selected tetraloop/receptors with previously unsolved structures (C7.2, C7.10, and R1). As a final test, SWM blindly and correctly predicted all noncanonical pairs of a Zika virus double pseudoknot during a recent community-wide RNA-Puzzle. Stepwise structure formation, as encoded in the SWM method, enables modeling of noncanonical RNA structure in a variety of previously intractable problems.