Summary: Let \(V\) be smooth variety defined over a discretely valued non-Archimedean field \(\mathbb K\) and let \(\phi:V \to V\) be a morphism on \(V\). In general a weak Néron model for a given pair \((V /\mathbb K, \phi)\) may not exist. The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field \(\mathbb K\) has a weak Néron model or not.