The general torque balance equations have been derived for the liquid crystal cells with weak anchoring boundaries by minimizing the bulk and surface free energy simultaneously [A. Sugimura, G. R. Luckhurst, and Z. Ou-Yang, Phys. Rev. E, 52, 681 (1995)]. The torque balance equations have been numerically solved to obtain the director distribution in the nematic liquid crystal cells with weak anchoring boundaries and the influence of the anchoring energy on the director distribution is elucidated.