By means of expressing the equilibrium configurations of high-beta tokamak plasmas analytically, the ideal MHD local stability criterion is derived with emphasis on the exploration of the possibility of existence of low-q, high-beta tokamaks. Results obtained show that a great variety of equilibria with these figures of merit may exist, some of them having great stability margin in the central region of the confined plasma against the local modes. Comparisons are made of results corresponding to configurations with different p′(ψ) and △(ρ) functions (△ being the displacement of the magnetic surface) and the tendency is found that the larger the displacement and the flatter the p′(ψ) profile is, the more stable the equilibrium will be.