In this paper, three different configurations of the Michelin's Tweel™, Resilient Technologies, and Bridgestone non-pneumatic tires (NPTs) are investigated by seeking compliant spoke structures. The quasi-static, two-dimensional analysis focuses on how the contact pressure, vertical tire stiffness and stresses are affected by the spoke structures and shear layer. Two cases of NPTs are investigated: (i) a tire with a composite ring and (ii) a tire without a composite ring. The results of the models were validated by comparison with four computational finite element models. The results showed that the shape of the spokes has a great effect on the tire's behavior in the second case, while the shear layer in the first case reduces the impact of the change of spokes shape especially in contact pressure distribution.