In this paper, we study the electromagnetic scattering from a two dimensional large rectangular open cavity embedded in an infinite ground plane, which is modelled by Helmholtz equations. By introducing nonlocal transparent boundary conditions, the problem in the open cavity is reduced to a bounded domain problem. A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases, respectively. A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hypersingular integral operator on the aperture and the Helmholtz in the cavity, respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers. A fast algorithm for the second-order approximation is proposed for solving the cavity model with layered media. Numerical results show the second-order accuracy and efficiency of the fast algorithm. More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.