Modern regulations concerning railway bridges are based on the approach of structural dynamics, which is described in PN-EN standards. This paper presents the results of theoretical dynamic analysis of the HSLM-A train set loading on the structure of a pre-stressed concrete arch bridge - the first railway bridge of its type which was built in Poland (completed in 1959). The recommendations of PN-EN have been followed and modal analysis was carried out to define the sensitivity of the structure to chosen eigenforms. Additionally the paper presents a course of calculations and the conclusions obtained from the analysis of displacements, accelerations, and bending moments induced in the structure through a simulated passage of a high-speed train in the context of the requirements of PN-EN Standards. The conclusions from the current calculations can be used for dynamic analysis of bridges of similar structural solutions.