In this thesis, an anchoring energy in the upper and lower substrates of TFT-LCD cell has been modeled and applied in the numerical calculation of the molecular orientation of the TN-LCD. The molecular orientation of liquid crystals defined as tilt and twist angles was simulated using the Newton-Raphson method and the Gaussian integration method. From the results, the tilt and twist angles for the strong anchoring energy were proven to be coincide with those of the conventional results. on the other hand, for the weak anchoring energy, azimuth angles of the molecules were changed abruptly from $0^{circ};to;90^{circ}$ near the middle area of the cell due to the balance of the anchoring energy and the elastic energy of the liquid crystals.