This paper describes physical meanings of various influences of cavity (or pillar) shape and filling factor of dielectric material on band structures in two-dimensional photonic crystals. Influences of circular and rectangular cross-sections of cavity (or pillar) arrays on photonic band structures are considered theoretically, and significant aspects of square and triangular lattices are compared. It is shown that both averaged dielectric constant of the photonic crystal and distribution profile of photon energy play important roles in designing optical properties. For the triangular lattice, especially, it is shown that cavity array with a rectangular cross-section breaks the band structure symmetry. So, we discuss this point from the band structure and address optical properties of lattice with a circular cross-section cavity.