TV reception antennas, such as Yagi array, installed above the roof are damaged by birds, storm and snow, and are not suitable for the house design. Beam tilted coupled loop antennas built in the roof tile were proposed to overcome these problems by the authors. This antenna element has a tilted beam pattern with very wide frequency bandwidth. This paper presents a FDTD analysis of this loop antenna backed by a dielectric material. The FDTD analysis is verified by experiments. However it requires a very long computation time and large computing resource to optimize antenna parameters. Therefore it is necessary to develop an analysis model for the antenna optimization with a short computation time and small computing resource. We then propose a MOM analysis using the effective dielectric constant for beam tilted coupled loop antennas built under the roof tile.