Optical power limiting has been observed in glass capillary arrays filled with liquid crystals. This behavior is attributed to optical field induced director reorientation and thermal effects. Dielectric measurements have been carried out to understand the director configurations and director reorientations of the liquid crystals in these near cylindrical glass microcapillaries. Different laser pulse durations from a CW Ar+laser and glass capillary arrays with different pore sizes have also been used in the optical power limiting measurements. Possible mechanisms are discussed and the relative contributions of different mechanisms are assessed.