We have already investigated stably stratified flows over a two-dimensional hill in a channel of finite depth by using a direct numerical simulation (DNS) at a Reynolds number of 2000, which is based on the uniform upstream velocity U and the hill height h. As a first step, we assumed a free-slip condition on the ground, both upstream and downstream of the hill, and imposed a no-slip condition only on the hill surface. Such a configuration corresponds to that of the previous towing tank experiments and numerical studies. For 1 < K(=NH/ π U) ≦2, the numerical results confirmed that the flow around the hill is intrinsically unsteady, which is manifested very clearly as periodic oscillations in the drag coefficient Cd on the hill. This flow unsteadiness is due mainly to the periodic shedding of upstream advancing columnar disturbances with mode n=l with a clockwise circulation. In the present study, as a next step, to investigate the flow around the hill under real atmospheric situations, we have performed calculations under an imposition of a no-slip condition on the ground, particularly focusing on the effect of stable stratifications on the unsteady separated and reattaching flow behind the hill for 0 ≦ K ≦ 1.3. The flow around the hill exhibits different behavior, corresponding to the difference in the boundary condition on the ground. For 0≦K≦0.9, the vortex shedding from the separation bubble behind the hill occurs. For K=l and 1.1, the vortex shedding is strongly suppressed so that the flow around the hill rapidly reaches an almost steady state. For K=l.2 and 1.3, although lee waves are excited downstream of the hill, the vortex shedding clearly exists. This is caused by the modification in the approaching flow just ahead of the hill, owing to the periodic shedding of columnar disturbances of mode n=l. The flow field with a vortex shedding shows an approximately steady state, corresponding to the stationary lee wave. The occurrence of local severe winds is observed near the lee side of the hill, which is caused by the downslope flow in the lee wave motion. From the investigation of time-averaged flow fields around the hill, the mean reattachment length of the separation bubble behind the hill becomes gradually longer as K approaches 1. The stable stratification effect inhibits the production of vorticity in the shear layer separating from the hill surface, leading to the gradual elongation in the size of the separation bubble behind the hill. However, this length is shortened again, mainly due to the appearance of the long lee wave with a strong downslope flow for 1 <K≦1.3.