There is a large number of old arch bridges in Iran's railway network which the majority of them have been built more than 70 years ago. These structures, though displaying a good performance under the effect of service (gravity) loads but the seismic (lateral) loads have not been taken into account in their design; therefore, the seismic assessment of these structures is deemed necessary for obtaining their failure and seismic performance levels. So they can be strengthened or rendered out of order in case it is found necessary. There are numerous methods for evaluating the residual capacity of the structures under seismic excitation which among them the non-linear dynamic analysis or the incremental dynamic analysis (IDA) is the most accurate and perfect method. Selecting 22 far-field earthquake records, the present study investigated two plain concrete arch bridges which are located in kilometers 23 and 24 of the old Tehran-Qom railway, respectively. By using the finite element method and the macro-modeling method the km-23 and km-24 bridges were simulated and totally 231 non-linear dynamic analyses have been conducted. The results obtained from the incremental dynamic analysis indicated that the seismic behavior of the bridge with longer span length is more vulnerable (km-23) than the bridge with lower span length (km-24). Generally, the seismic performance of plain concrete arch bridges has been found inappropriate, therefore to improve their performance it is necessary to retrofit these type of structures.