Computer simulation is carried out for the structural evolution of semidilute suspensions of non-Brownian, rodlike particles under shear flow. The short-range part of the hydrodynamic interaction is taken into account by the lubrication approximation, but the long-range part is neglected. For this model, the effect of the hydrodynamic interaction is found to be small. The major conclusions are (i) the excess viscosity is proportional to the number density n even in the region nL(3) approximate to 40, where L is the length of the rod; (ii) the Folgar-Tucker constant C, which represents the deviation of each rod from the Jeffery orbit due to the hydrodynamic interaction, is of the order 10(-7) similar to 10(-4). Implications of these results in conjunction with existing theories and experiments are discussed.