Fault diagnosis and condition monitoring of synchronous machines running under load is a key determinant of their lifespan and performance. Faults such as broken rotor bars, bent shafts and bearing issues lead to eccentricity faults. These faults if not monitored may lead to repair, replacement and unforeseen loss of income. Researchers who attempted to investigate this kind of machine stopped at characterizing and deduced ways, types and effects of rotor eccentricity fault on the machine inductances using the winding function method. A modified closed-form analytical model of an eccentric synchronus reluctance motor (SynRM) is developed here taking into cognizance the machine dimensions and winding distribution for the cases of a healthy and unhealthy SynRM. This paper reports the study the SynRM under static rotor eccentricity using the developed analytical model and firming up the model with finite element method (FEM) solutions. These methods are beneficial as they investigated and presented the influence of the degrees of static eccentricity on the machine performance indicators such as speed, torque and the stator