Conventional statistical shape models use Principal Component Analysis (PCA) to describe shape variations. However, such a PCA-based model assumes a Gaussian distribution of data. A model with Independent Component Analysis (ICA) does not require the Gaussian assumption and can additionally describe the local shape variation. In this paper, we propose a Hierarchical Constrained Local Model (HCLM) using ICA. The first or coarse level of HCLM locates the full landmark set, while the second level refines a relevant landmark subset. We then apply the HCLM to Down syndrome detection from photographs of young pediatric patients. Down syndrome is the most common chromosomal condition and its early detection is crucial. After locating facial anatomical landmarks using HCLM, geometric and local texture features are extracted and selected. A variety of classifiers are evaluated to identify Down syndrome from a healthy population. The best performance achieved 95.6% accuracy using support vector machine with radial basis function kernel. The results show that the ICA-based HCLM outperformed both PCA-based CLM and ICA-based CLM.