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This work presents an algorithm for the unsupervised learning, or induction, of a simple morphology of a natural language. A probabilistic maximum a posteriori model is utilized, which builds hierarchical representations for a set of morphs, which are morpheme-like units discovered from unannotated text corpora. The induced morph lexicon stores parameters related to both the “meaning” and “form” of the morphs it contains. These parameters affect the role of the morphs in words. The model is implemented in a task of unsupervised morpheme segmentation of Finnish and English words. Very good results are obtained for Finnish and almost as good results are obtained in the English task.