Semantic parsing is the task of transducing natural language (NL) utterances into formal meaning representations (MRs), commonly represented as tree structures. Annotating NL utterances with their corresponding MRs is expensive and time-consuming, and thus the limited availability of labeled data often becomes the bottleneck of data-driven, supervised models. We introduce StructVAE, a variational auto-encoding model for semi-supervised semantic parsing, which learns both from limited amounts of parallel data, and readily-available unlabeled NL utterances. StructVAE models latent MRs not observed in the unlabeled data as tree-structured latent variables. Experiments on semantic parsing on the ATIS domain and Python code generation show that with extra unlabeled data, StructVAE outperforms strong supervised models.