Abstract Current business trends push transport companies to improve the efficiency of their entrepreneurial activities, what is closely related to costs reduction and revenues increase. Many transport companies achieve it empirically, but some mathematical algorithms, mainly from operational research, can be used to improve the efficiency of railway transport by finding the optimal solution of specific problems. The paper is focused on using of selected methods from applied mathematics in railway transport. These methods are used mainly for improving the operational efficiency of the transport company, what tends to decrease overall operating costs. Major impact is done by efficient use of railway vehicles and train staff. It can be achieved by optimization as a flow network problem or assignment problem, what is further described in the paper. Mathematical approaches can also positively influence the whole logistic process.