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Parametric point clouds are sampled from CAD shapes and are becoming increasingly common in industrial manufacturing. Most CAD-specific deep learning methods focus on geometric features, while overlooking constraints inherent in CAD shapes. This limits their ability to discern CAD shapes with similar appearances but different constraints. To tackle this challenge, we first analyze the constraint importance via simple validation experiments. Then, we introduce a deep learning-friendly constraint representation with three components, and design a constraint-aware feature learning network (CstNet), which includes two stages. Stage 1 extracts constraint representation from BRep data or point cloud based on local features. It enables better generalization ability to unseen dataset after pre-training. Stage 2 employs attention layers to adaptively adjust the weights of three constraints' components. It facilitates the effective utilization of constraints. In addition, we built the first multi-modal parametric-purpose dataset, i.e. Param20K, comprising about 20K CAD instances of 75 classes. On this dataset, CstNet achieved 3.49% (classification) and 26.17% (rotation robustness) accuracy improvements over the state-of-the-art. To the best of our knowledge, CstNet is the first constraint-aware deep learning method tailored for parametric point cloud analysis.