The shares will be offered at a starting price of 850 marka ($471.7/434.6 euro), Zeljeznice RS said in a bourse filing.
The shares offered for sale represents a 1% stake in the company. The company's share capital is divided into 50,000 shares of 1 marka in par value each.
The company's shares last traded on the Banja Luka bourse on May 21, closing flat at 75 marka.
The Serb Republic is one of the two autonomous entities that form Bosnia and Herzegovina. The other entity is the Federation.
(1 euro = 1.956 marka)