In this paper, we present a predictive and generative design approach for supporting the conceptual design of product shapes in 3D meshes. We develop a target-embedding variational autoencoder (TEVAE) neural network architecture, which consists of two modules: (1) a training module with two encoders and one decoder (E2D network) and (2) an application module performing the generative design of new 3D shapes and the prediction of a 3D shape from its silhouette. We demonstrate the utility and effectiveness of the proposed approach in the design of 3D car body and mugs. The results show that our approach can generate a large number of novel 3D shapes and successfully predict a 3D shape based on a single silhouette sketch. The resulting 3D shapes are watertight polygon meshes with high-quality surface details, which have better visualization than voxels and point clouds, and are ready for downstream engineering evaluation (e.g., drag coefficient) and prototyping (e.g., 3D printing).