A complete derivation of the moment equations of a Vlasov plasma has been presented separately for the three density domains, namely the high-density regime (b→0), the moderate-density regime [b ≃ O(1)] and the low-density regime [b2 ≃ O(1)] with b as the ratio of Alfvén velocity to light velocity and = a/L where a is the ion Larmor radius and L, the characteristic length of the system. These moment equations are then employed to investigate the effect of finite β (= particle pressure/magnetic pressure) on gravitational flute instability of a non-uniform plasma. It is shown that the effect of finite β is one of stabilization.