Employing a coupled model for vehicle-track interaction, this paper presented the dynamic analysis of railway track system in the presence of weld irregularities with different geometric profiles in two parallel rails. A 3D model of a standard railway wagon running on a ballasted track system is used to examine the vibrations of the system under track irregularities. Four samples of measured rail profiles at rail welds are considered as the source of dynamic excitations, in which the profiles of parallel rails are unequal. Hence, the individual profiles of left/right rails are imported into the numerical model, taking into account the nonuniform conditions of rail welds in both sides of the railway track. The dynamic responses of the track system caused by irregularities at welds are studied by performing the time-domain vibration analysis. The time histories of the nodal responses under various weld scenarios (measured in an actual railway track site) are recorded. Finally, the peak responses of dynamic forces along the track are determined for left/right rails. The results of dynamic simulations in various weld scenarios are compared and the values of dynamic amplification factors (DAFs) are evaluated. Such findings provide an estimation for the levels of dynamic forces occurring under impact loading conditions of nonuniform rail welds in left/right rails.