One of the leading issues facing the railway sector is the occurrence of rolling contact fatigue fractures on the surfaces of the rail, its weld, and wheels. In the present study, a FEM model was investigated on an Aluminium-Thermite weld to estimate the beginning of fatigue cracks. The investigated model comprises a FEM analysis that accounts for the material behaviour due to the contact pressure between the rail weldment and the running wheel. The rail with its weldment and the wheel is modelled using FEM in ANSYS space-claim with a squat type of semi-elliptical crack. Force is applied vertically on the wheel's axle, then rolled on the rail weld assembly in the longitudinal direction. The resulting stress and strain values for the critical plane were integrated with the life calculation model under multi-axial fatigue to estimate the beginning of fatigue cracks. The study also estimates fatigue damage parameters at the contact region. To initiate the crack initiation, a fracture length of 0.5 mm on the curve of the weld was considered, and the cycle calculation was obtained. The maximum contact pressure is estimated to be approximately 2×106 cycles. The study involves two sub-models for analysis with different boundary conditions, revealing the numerical prediction of initiation of 0.5 mm-long cracks with cycle counts as 7.47×106 cycles for Model-I and 3.87×106 cycles for Model-II. Results are validated with other literature findings and proposed modifications.