This article presents a description of the Modern Greek Noun Phrase (NP) using the 'Affix Grammars over a Finite Lattice' formalism. This work, carried out within the framework of a Ph.D. dissertation, constitutes a first attempt at computational processing of Modern Greek using a corpus-oriented system. The formal description of the Modern Greek NO is developed in order to verify in a NP corpus the respective hypothesis/linguistic analysis on which is based. The hypothesis/linguistic analysis adopts a descriptive point of view and focuses on the surface structure of the NP. Both the hypothesis/linguistic analysis and the formal description describe different structures of the NP and handle the peculiarities of the Modern Greek NP as well as gapping and ambiguity phenomena which occur in co-ordinated structures, satisfying the criteria of description adequacy and flexibility. The testing of the formal description on a carefully selected corpus has proven that most types of the Modern Greek NPs, as well as co-ordinated and appositive structures, can be analysed with a high degree of success.