The Constraint Network Analysis (CNA) web server provides a user-friendly interface to the CNA approach developed in our laboratory for linking results from rigidity analyses to biologically relevant characteristics of a biomolecular structure. The CNA web server provides a refined modeling of thermal unfolding simulations that considers the temperature dependence of hydrophobic tethers and computes a set of global and local indices for quantifying biomacromolecular stability. From the global indices, phase transition points are identified where the structure switches from a rigid to a floppy state; these phase transition points can be related to a protein's (thermo-)stability. Structural weak spots (unfolding nuclei) are automatically identified, too; this knowledge can be exploited in data-driven protein engineering. The local indices are useful in linking flexibility and function and to understand the impact of ligand binding on protein flexibility. The CNA web server robustly handles small-molecule ligands in general. To overcome issues of sensitivity with respect to the input structure, the CNA web server allows performing two ensemble-based variants of thermal unfolding simulations. The web server output is provided as raw data, plots and/or Jmol representations. The CNA web server, accessible at http://cpclab.uni-duesseldorf.de/cna or http://www.cnanalysis.de, is free and open to all users with no login requirement.