In any NDE application, the availability of a theoretical model is very useful in understanding the capability of the system since it can enable the visualization of field/flaw interaction for different flaw and sensor geometries. A numerical model capable of simulating inspection of multi-layered structures using eddy current excitation and magneto-resistive sensing is developed to predict 2D image data of rivet locations. The model is used to study particularly the effect of sensor tilt on the probability of detection (POD) of defects at rivet sites. The modeling of sensor-tilt during inspection around rivet sites has to take into account finite source coil and meshing of the finite source coil at each scan position. This paper presents a finite element (FE) model formulation using reduced magnetic vector potential and electric scalar potential in a way that does not require meshing source coils. In addition to simulating the effect of sensor tilt on the signal, this paper also describes features in the signal that are invariant to sensor tilt but sensitive to defect parameters.