Abstract: In this Papar, the reflection and transmission Properties of EM waves incident on a inhomogeneous and lossy plasma sheath with arbirary profile are discussed by using finite element method,The prarameters of profile takes of the fluid fields data of viscus shock layer for a typical re-entry vehicles.Starting from the virtual work principle,first of all,the variational equ-ation of EM propagation throush the plasma sheath is derivated and then the finite element equation is developed from the veriational equation,The element matrix for EM propagation through the plasma sheath with an arbitrary profile is constructed by applying a function of linear interpolation and numerical results are discussed. Our conclusion is that the FEM is suitable for computation of radio waves through plasma sheath with an arbitrary variable profile.