Identification of fusion proteins has contributed significantly to our understanding of cancer progression, yielding important predictive markers and therapeutic targets. While fusion proteins can be potentially identified by mass spectrometry, all previously found fusion proteins were identified using genomic (rather than mass spectrometry) technologies. This lack of MS/MS applications in studies of fusion proteins is caused by the lack of computational tools that are able to interpret mass spectra from peptides covering unknown fusion breakpoints (fusion peptides). Indeed, the number of potential fusion peptides is so large that the existing MS/MS database search tools become impractical even in the case of small genomes. We explore computational approaches to identifying fusion peptides, propose an algorithm for solving the fusion peptide identification problem, and analyze the performance of this algorithm on simulated data. We further illustrate how this approach can be modified for human exons prediction.