Abstarct: Superconducting synchronous machines have different structures that the most common type consists of a rooming stator core with the regular copper coils, and cold-core rotor with superconducting coils. In this structure, for stay on the superconducting mode of the rotor coil, some troublemaker factors such as the harmonics of the stator field and air gap field distortions especially in the case of transient state exist. So for solving these problems, a conductive shield which covering core and rotor coil is provided to eliminate the field distortion on the rotor. Due to complex topology of the magnetic circuit of electric machine, the accurate calculation of flux lixnkage of the damper laxyer is very difficult or impossible by analytical methods. So the most precise and practical solution for calculation of the current distribution in damper shield, is utilizing a numerical method such as the finite element method. Thickness of damper shield, with a preliminary argument, usually is a percentage of the influence depth of the stator magnetic field in steady state while stay on the superconducting mode of coil rotor in transient state is more important, and for determining the thickness of damper shield, accurate analysis of machine performance in transient conditions is required. Therefore, to solve the problem of determining the thickness of damper shield, performance characteristics of a superconducting synchronous machine in transient state is reviewed by 2-D modeling of machine by utilizing transient FEM capability of a finite element software. in this thesis, analysis of effect of different thicknesses damper shield on superconductor synchronous machine treatment with study of characteristics machine performance and finally by showing eddy current density colored distribution on the surface of conductive damper shield with purpose of diagnosis influence depth of magnetic field, optimal design of electro-magnetic damper shield, for the first time, is determined by considering the different positions for damper laxyer in air-gap. Comparing the results of this method, with the previous studies represent an acceptable accuracy. JMAG Designer software is used for finite element modeling.