Magnetohydrodynamic (MHD) equilibrium states with a three-dimensional helical core that display the characteristics of a saturated ideal internal kink mode are computed to model snake structures that have been observed in the JET tokamak [A.~Weller et al. 1987 Phys.~Rev.~Lett.~ extbf{59} 2303]. The equilibrium states are calculated with a peaked pressure profile and a weak to moderate reversed core magnetic shear with a minimum safety factor $q_{min}$ near unity in the neighbourhood of the mid-radius of the plasma. Snake equilibrium states are computed in the range $0.94