We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions separated by ideal magnetohydrodynamic (MHD) barriers. A principal motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically three-dimensional equilibria, with non-zero internal pressure. A second application is the description of transport barriers as constrained minimum energy states. As a first example, we calculate the plasma solution in a periodic cylinder, generalizing the analysis of the treatment of Kaiser and Uecker (2004 Q. J. Mech. Appl. Math.57, 1–17), who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak-like equilibria, with increasing safety factor and stepped-pressure profiles.