In this paper the mechanism of a cosmological phase transition is addressed in a new way which avoids weaknesses of previous approaches. The effects of inhomogeneities are included explicitly. A numerical analysis is presented in which for a wide class of models the Universe enters a period of new inflation. The analysis is classical and applies to models in which the scalar field responsible for driving inflation is weakly coupled to other fields. We derive heuristic arguments which determine the boundaries of the region in parameter space for which inflation is realized. The agreement with the numerical results is good. This paper complements a previous analytical analysis.