SummaryIn this study, we propose constructive ways to determine input‐to‐state stability (ISS) as well as incremental ISS (δISS) of nonpolynomial dynamical systems. The developed procedures are based on sums‐of‐square decomposition. This tool is only applicable to polynomial systems. Thus, a rational recast of the nonpolynomial system description is used. This recast generally leads to an increased system order and additional constraints. These constraints must be respected in the resulting formulations. The proposed approach gives a unique and constructive procedure to determine the ISS and the δISS property, which is normally nontrivial and needs a good understanding of the system's dynamics. The proposed approaches are illustrated on several examples.