This paper describes the development and evaluation of a FST-based analyser-generator for Mapudüngun language, which is publicly available through a web interface. As far as we know, it is the first system of this kind for Mapudüngun. Following the Mapuche grammar by Smeets, we have developed a machine including the morphological and phonological aspects of Mapudüngun. Through this computational approach we have produced a finite state morphological analyser-generator capable of classifying and appropriately tagging all the components (roots and suffixes) interacting in a Mapuche word-form. A double evaluation has been carried out showing a good level of reliability. In order to face the lack of standardization of the language, additional components (an enhanced analyser, a spelling unifier and a root guesser) have been integrated in the tool. The generated corpora, the lexicons and the FST grammars are available for further development and comparison results.