An equilibrium solution correct to the second order of the inverse aspect ratio is obtained for the axisymmetric Tokamak with circular cross section. The toroidal current density distribution profile is non-uniform. The equilibrium parameters are computed. The values of the displacement of the magnetic axis xm and the limiting value of the poloidal beta beta P,max are determined. The optimum toroidal current density profile is found. The second order correction increases the value of beta P,max and decreases the value of xm. The shape of the conducting shell surrounding the plasma is estimated.