[en] The magnetohydrodynamic equilibrium states by Hill's vortex model and by the Coulomb-wave-function model are proved to be unstable. New MHD equilibrium configurations are determined by using another model for which dp/dψ = 0 on the magnetic axis. Here p is the pressure and ψ is the flux function. The values of the safety factor on the magnetic axis, q_axis, are evaluated for these configurations. The MHD stability of these equilibrium states is investigated by the Mercier criterion. The values of the maximum beta ratio β_max are evaluated for this model. The optimized pressure distributions are determined by use of the Mercier criterion and the values of β_max are also evaluated for these pressure distributions. The values of β_max are shown to be at most 12 %, if the condition q_axis < 1 is required. (author)