Whole-genome sequencing resolves many clinical cases where standard diagnostic methods have failed. However, at least half of these cases remain unresolved after whole-genome sequencing. Structural variants (SVs; genomic variants larger than 50 base pairs) of uncertain significance are the genetic cause of a portion of these unresolved cases. As sequencing methods using long or linked reads become more accessible and SV detection algorithms improve, clinicians and researchers are gaining access to thousands of reliable SVs of unknown disease relevance. Methods to predict the pathogenicity of these SVs are required to realize the full diagnostic potential of long-read sequencing. To address this emerging need, we developed StrVCTVRE to distinguish pathogenic SVs from benign SVs that overlap exons. In a random forest classifier, we integrated features that capture gene importance, coding region, conservation, expression, and exon structure. We found that features such as expression and conservation are important but are absent from SV classification guidelines. We leveraged multiple resources to construct a size-matched training set of rare, putatively benign and pathogenic SVs. StrVCTVRE performs accurately across a wide SV size range on independent test sets, which will allow clinicians and researchers to eliminate about half of SVs from consideration while retaining a 90% sensitivity. We anticipate clinicians and researchers will use StrVCTVRE to prioritize SVs in probands where no SV is immediately compelling, empowering deeper investigation into novel SVs to resolve cases and understand new mechanisms of disease. StrVCTVRE runs rapidly and is publicly available.