A numerical model of a magnetic shield type superconducting fault current limiter based on an integral formulation of the coupled electromagnetic-thermal problem is presented. A step-by-step linearization of the magnetic problem is introduced in order to solve the system. A simplified equivalent circuit is introduced and implemented inside the Electromagnetic Transient Program power system simulator. The results of the simplified and the full model are compared and the error is evaluated. Index Terms-Coupled problem, Electromagnetic Transient Program (EMTP), equivalent circuit, magnetic shield type fault current limiter (FCL), nonlinear magnetostatics, power system simulator, superconducting fault current limiter (SFCL).