This paper describes a preliminary experiment in designing a Hidden Markov Model (HMM)‐based part‐of‐speech tagger for the Lithuanian language. Part‐of‐speech tagging is the problem of assigning to each word of a text the proper tag in its context of appearance. It is accomplished in two basic steps: morphological analysis and disambiguation. In this paper, we focus on the problem of disambiguation, i.e., on the problem of choosing the correct tag for each word in the context of a set of possible tags. We constructed a stochastic disambiguation algorithm, based on supervised learning techniques, to learn hidden Markov model's parameters from hand‐annotated corpora. The Viterbi algorithm is used to assign the most probable tag to each word in the text.