The approximate description of tokamak plasma evolution during fast heating is discussed. The equilibrium configuration of two important types of flux-conserving evolution of tokamak plasma are obtained: the adiabatic compression and the noncom-pressional fast heating. It is assumed that the plasma shape is noncircular with small arbitrary deformations from the average circles and there exists only one elliptic magnetic axis for the initial configuration. By means of expansion of the plasma parameters in terms of the inverse aspect ratio the problem becomes tractable analytically. It is demonstrated that this method can be used successfully to describe the evolution sequence of adiabatic compression; as far as the noncompressional fast heating is concerned. The results are also in consistence with that of two-dimensional computation if the displacement of the magnetic axis (or the poloidal beta value) remains not very large.