In this paper we analyzed the electromagnetic behavior of high $-T_{c}$ superconductor under the quench state using finite element method. Poisson equation was used in finite element analysis as a governing equation and was solved using algebra equation using Gallerkin method. We first investigate d the electromagnetic behavior of U-type superconductor. Finally we applied our analysis techniques to 5.5 kVA meander-line superconducting fault current limiters (SFCL) which are currently developed by many power-system researcher in the world. Meshes of 14,600 elements were used in analysis of this SFCL. Analysis results show that the distribution of current density was concentrated to inner curvature in meander-line type-superconductors and maximum current density 14.61 $A/m^2$ and also maximum Joule heat was 6,420 W/㎥. We concluded that this meander line-type SFCL was not pertinet fur uniform electromagnetic field distribution.n.