Parametric point clouds are sampled from CAD shapes and are becoming increasingly common in industrial manufacturing. Most existing CAD-specific deep learning methods only focus on geometric features, while overlooking constraints which are inherent and important in CAD shapes. This limits their ability to discern CAD shapes with similar appearance but different constraints. To tackle this challenge, we first analyze the constraint importance via a simple validation experiment. Then, we introduce a deep learning-friendly constraints representation with three vectorized components, and design a constraint-aware feature learning network (CstNet), which includes two stages. Stage 1 extracts constraint feature from B-Rep data or point cloud based on shape local information. It enables better generalization ability to unseen dataset after model 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 shape instances of 75 classes. On this dataset, we performed the classification and rotation robustness experiments, and CstNet achieved 3.52\% and 26.17\% absolute improvements in instance accuracy over the state-of-the-art methods, respectively. To the best of our knowledge, CstNet is the first constraint-aware deep learning method tailored for parametric point cloud analysis in CAD domain.