Genomic　micro-satellites　are　the　genomic　regions　that　consist　of　short　and　repetitive　DNA　motifs.　In　contrast　to　unique　genome,　genomic　micro-satellites　expose　high　intrinsic　polymorphisms,　which　mainly　derive　from　variability　in　length.　Length　distributions　are　widely　used　to　represent　the　polymorphisms.　Recent　studies　report　that　some　micro-satellites　alter　their　length　distributions　significantly　in　tumor　tissue　samples　comparing　to　the　ones　observed　in　normal　samples,　which　becomes　a　hot　topic　in　cancer　genomics.　Several　state-of-the-art　approaches　are　proposed　to　identify　the　length　distributions　from　the　sequencing　data.　However,　the　existing　approaches　can　only　handle　the　micro-satellites　shorter　than　one　read　length,　which　limits　the　potential　research　on　long　micro-satellite　events.　In　this　article,　we　propose　a　probabilistic　approach,　implemented　as　ELMSI　that　estimates　the　length　distributions　of　the　micro-satellites　longer　than　one　read　length.　The　core　algorithm　works　on　a　set　of　mapped　reads.　It　first　clusters　the　reads,　and　a　k-mer　extension　algorithm　is　adopted　to　detect　the　unit　and　breakpoints　as　well.　Then,　it　conducts　an　expectation　maximization　algorithm　to　approach　the　true　length　distributions.　According　to　the　experiments,　ELMSI　is　able　to　handle　micro-satellites　with　the　length　spectrum　from　shorter　than　one　read　length　to　10　kbps　scale.　A　series　of　comparison　experiments　are　applied,　which　vary　the　numbers　of　micro-satellite　regions,　read　lengths　and　sequencing　coverages,　and　ELMSI　outperforms　MSIsensor　in　most　of　the　cases.　©　2018,　Springer　International　Publishing　AG,　part　of　Springer　Nature.