A non-pneumatic tire (NPT) has two advantages over a conventional pneumatic tire; it is flat proof and maintenance free of air-pressure. In this study, while determining other advantages inherent in NPTs, the static contact behavior of NPTs with hexagonal honeycombs is investigated as a function of vertical loading and is compared with that of a pneumatic tire. A finite element based numerical simulation is carried out on the contact pressure of NPTs with cellular spokes and the local deformation of cellular spokes. A commercial finite element code, ABAQUS, is used to vary the vertical forces and lattice spoke geometries. A lower contact pressure is obtained with the NPTs than with the pneumatic tire due to the decreasing spoke stiffness of the NPTs when they are designed to have the same load carrying capability. An NPT with hexagonal lattice spokes having a higher cell angle shows a lower local cell wall stress in the spokes, associated with the flexible honeycomb property in uni-axial compression.