Abstract: Two schemes for vertical discretization of the model are proposed,one with equal lna in-terval and the other in terms of Tschebyscheff polynomial.It is proved that in adiabatic and inviscid case if the meteorological elements are continuous in time and horizontal direction the total energy and total mass are conserved in high approximation,and there is a correct conversion between kinetic and total potential energy.Numerical computations show that the schemes both have highaccuracy.For example.in integrating the hydrostatic equation the computational errors of geopotential resulted from the schemes are much less than those resulted from EC79.