In this thesis the magnetic properties of a type- II Superconducting disk which carries a radial traort current and is in a periodic magnetic field has been investigated. The field is applied perpendicular to the surface of disk. For this study, the critical state model (CSM) Bean, Kim and exponential are used. In Bean model where critical current density is assumed to be independent of local field, the magnetization, magnetic hysterics loops and ac susceptibility have been investigated. The results of Bean model shows that the magnetic flux will penetrate in all parts of the disk, when the thin superconductor disk in the absence of a radial traort current is subjected to the strong magnetic field perpendicular to the surface of disk. When the applied field is turned off and radial traort current fed simultaneously into the disk, the vortices are expelled from the disk and disk's central region becomes resistive. On the other hand, an increase in magnetic field, applied perpendicularly surface of disk at initially with no vortices caused the penetration of vortices into the disk. Vortices penetrates until the Lorentz force equals the pinning force. A further increase in the applied magnetic field, causes the vortices to be pushed into the disk. Namely the vortices are driven suddenly towards the center of the disk. At the end of second stage where is a temporary stage, disk's central region becomes resistive. Gradually increasing the magnetic field leads to a condensation of the vortex lattice. In addition to the Bean model the magnetic properties of a superconductor has been investigated using Kim and exponential models. The main difference between results of Kim and exponential and results of Bean model is the number of stages of flux penetration into the disk. Our calculations show that flux penetration into the disk can occur in three stages or one.