To more accurately simulate the pressure distribution of the ultra-thin air bearing film, Reynolds equation must be modified to account for the gas rarefaction effect. Starting from a widely used model of Reynolds equation, a new simplified second order model is proposed to simulate the ultra-thin air bearing film in hard disk drives. The new model of Reynolds equation possesses simpler mathematical form than that of the previous model. The new model is solved using a least square finite difference method and the resultant numerical results are compared with those of the previous model. The computational efficiencies of the new model and the previous model are also compared.