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RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires knowledge of their tertiary structures. Though computational RNA folding approaches exist, they often require manual manipulation and expert intuition; predicting global long-range tertiary contacts remains challenging. Here we develop a computational approach and associated program module (RNAJAG) to predict helical arrangements/topologies in RNA junctions. Our method has two components: junction topology prediction and graph modeling. First, junction topologies are determined by a data mining approach from a given secondary structure of the target RNAs; second, the predicted topology is used to construct a tree graph consistent with geometric preferences analyzed from solved RNAs. The predicted graphs, which model the helical arrangements of RNA junctions for a large set of 200 junctions using a cross validation procedure, yield fairly good representations compared to the helical configurations in native RNAs, and can be further used to develop all-atom models as we show for two examples. Because junctions are among the most complex structural elements in RNA, this work advances folding structure prediction methods of large RNAs. The RNAJAG module is available to academic users upon request.