In this paper we present the first results of the application of computational methods, inspired by the ideas in McMahon & McMahon (2005), to a dataset collected from languages of every branch of the Tupian family (including all living non-Tupí-Guaraní languages) in order to produce a classification of the family based on lexical distance. We used both a Swadesh list (with historically stabler terms) and a list of animal and plant names for results comparison. In addition, we also selected more (HiHi) and less (LoLo) stable terms from the Swadesh list to form sublists for indepedent treatment. We compared the resulting NeighborNet networks and neighbor-joining cladograms and drew conclusions about their significance for the current understanding of the classification of Tupian languages. One important result is the lack of support for the currently discussed idea of an Eastern-Western division within Tupí.