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Background: Short tandem repeats are ubiquitous in genomic sequences and due to their complex evolutionary history pose a challenge for sequence alignment tools., Results: To better account for the presence of tandem repeats in pairwise sequence alignments, we propose a simple tractable pair hidden Markov model that explicitly models their presence. Using the framework of gain functions, we design several optimization criteria for decoding this model and describe resulting decoding algorithms, ranging from the traditional Viterbi and posterior decoding to block-based decoding algorithms tailored to our model. We compare the accuracy of individual decoding algorithms on simulated and real data and find that our approach is superior to the classical three-state pair HMM., Conclusions: Our study illustrates versatility of pair hidden Markov models coupled with appropriate decoding criteria as a modeling tool for capturing complex sequence features.