Following a theoretical analysis of the scope of Nash implementation for a given mechanism, we study the formal framework for computational identification of Nash implementability. We provide computational tools for Nash implementation in finite environments. In particular, we supply Python codes that identify (i) the domain of preferences that allows Nash implementation by a given mechanism, (ii) the maximal domain of preferences that a given mechanism Nash implements Pareto efficiency, (iii) all consistent collections of sets of a given social choice correspondence (SCC), the existence of which is a necessary condition for Nash implementation of this SCC, and (iv) check whether some of the well-known sufficient conditions for Nash implementation hold for a given SCC. Our results exhibit that the computational identification of all collections consistent with an SCC enables the planner to design appealing mechanisms. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.