Active faults in the earthquake region are consistently regarded as a potential geological hazard to the construction and operation of railway engineering. However, crossing active faults is always difficult to be avoided for railway construction. In this paper, three-dimensional finite element models are established to study the behaviors of the railway embankment under normal faulting. The constitutive model used in the soil layer is validated by using the data of the centrifuge tests from the existing paper. A series of parametric studies are conducted considering the faulting offset, the thickness of the soil layer, the dip angle of the fault and the cross-fault angle of the embankment. Emphasis is given to (1) the affected zones; (2) the vertical displacement, the longitudinal slope, the lateral displacement, and the radius of the curvature of the embankment centerline; (3) the potential regions where the fault ruptures outcrop based on the plastic strain; (4) the stress characteristic of the embankment surfaces. The analysis shows that the increase of faulting offset would increase the value of longitudinal slope in the cross-fault region of the embankment. The existence of soil layer and its thickening would widen the affected zones and the regions where the fault ruptures outcrops. The fault dip angle and the cross fault angle of the embankment have a complex effect on the behaviors of the crossing embankment. The depth of the subsidence zone of the embankment would increase with the decrease of fault dip angle and the large fault dip angle would change the primary fault rupture to be a compressive one directly above the fault line. If the embankment crosses the fault line obliquely, the curvature radius of the centerline would hardly meet the design code.