Most machine translation systems apply to written, standardized language varieties. In contrast, we present a model that takes into account some specificities of dialects: - Dialect areas show continuous variation along all levels of linguistic analysis; it is linguistically not satisfactory to model a finite number of distinct dialects as if they were unrelated languages. - Written dialectal data is often not available in sufficient quality and quantity; however, we can rely on atlases, dictionaries and grammars compiled by dialectologists. - Most dialects are closely related to a resource-rich standardized language (in our case, Standard German). We argue that machine translation into Swiss German dialects is best modelled by a traditional rule-based transfer system that can be parametrized by probabilistic geographical maps. We show how such maps can be extracted from dialectological atlases. We will also discuss some issues related to the evaluation of multidialectal machine translation.