This paper deals with the treatment of stress in Greek inflectional morphology. First, a morphological processor is presented which is built on the basis of a linguistic analysis of Greek inflected forms. This is followed by a discussion of how stress applies to words and how stress shift phenomena are taken into account by the morphological processor. In Greek, word stress distribution is important because it represents a major difficulty in every attempt to create a morphological processor which can be used by speech recognition systems, machine readable dictionaries, and machine translation projects involving Greek as source or target language.