In this paper, we analysed companies whose shares are included in the Republic of Srpska Stock Exchange Index (BIRS), using Altman's Z-Score model and Altman's Z"-Score model, in order to determine their insolvency risk. Altman's Z-Score is a combination of five weighted financial ratios used to estimate the likelihood of financial distress, and possible bankruptcy of the observed companies. It is used widely by auditors, accountants, commercial banks, and other organizations to assess the financial health of their clients. Altman also developed revised versions of the model to assess the financial health of privately-held firms and non-manufacturing companies, as well as companies in emerging markets - Altman's Z'- Score model and Altman's Z" - Score model. The results of our research on a sample of 14 companies whose shares are included in BIRS show that, although it is an emerging market, Altman's Z-Score model gives better results that indicate much-needed caution when drawing conclusions about the observed companies.