This paper presents a new approach to solve two-dimensional transverse magnetic (TM) scattering problems involving homogeneous penetrable scatterers. The scatterers can be replaced by equivalent electric surface currents provided a proper surface admittance operator is introduced relating those currents to the electric fields on the scatterer's surface. The surface operator for a scatterer with rectangular cross section can be determined analytically. The paper emphasizes that the proposed technique remains valid in a complex scattering environment and in the presence of both conducting and nonconducting scatterers. The new method allows for a considerable gain in CPU time and memory requirements and remains very accurate even in the presence of very good conductors and this from the DC regime to the high-frequency skin effect regime. Scattering of a plane wave by a periodic arrangement of rectangles or crosses embedded in a dielectric slab is used to illustrate the use of the surface admittance operator in conjunction with an integral equation method.