The dynamic performance of a ground vehicle is predominantly influenced by interactions of the tires with the terrain. The designs of pneumatic tires has evolved over the past many decades to satisfy multiple performance demands such as transfer of tractive/braking forces with minimal energy losses, ease of handling and directional control, ride comfort and road holding. Despite their proven superior performance, the pneumatic tires exhibit deficiencies such as loss of vehicle performance and directional control in the event of severe air leakage or bursting, high maintenance, complex manufacturing process, and fire hazards and environmental risks of used tires. In recent years, concepts in non-pneumatic wheels (NPWs) with different spokes’ designs have emerged, which potentially offer many advantages over the pneumatic tires, particularly the elimination of the road safety risks and the routine maintenance induced by the inflation pressure loss. The reported studies on NPWs with honeycomb spokes have mostly focused on their static and dynamic responses to normal wheel loads, such as vertical deflection, modes of vibration and rolling resistance. Only minimal efforts, however, are evident in view of their out-of-plane responses such as cornering force and self-aligning moment, which are vital for adequate handling and directional control of the vehicle. This dissertation research is focused on design and development honeycomb NPWs with an objective to achieve in-plane and out-of-plane force-deflection and force-slip characteristics comparable to those of the pneumatic tires so as to be considered as their potential substitute in general vehicular applications. Three-dimensional finite element (FE) models of the honeycomb NPW with different spokes’ configurations are initially developed using ABAQUS software in order to predict their static and dynamic responses. A mesh convergence study is conducted to determine nearly optimal element sizes for each component, which permitted convergence of responses with least computational cost. The validity of these wheel models is verified by comparisons of predicted responses with the available results. The verified NPW models are subsequently employed to evaluate their feasibility and relative merits through comparisons of in-plane as well as out-of-plane properties with those of a reference pneumatic tire (205/55R16). These include the multi-axis stiffness properties as well as cornering force and self-aligning moment characteristics. It is shown that the honeycomb NPW designs could be easily tuned with to achieve vertical and longitudinal stiffness as those of the reference pneumatic tire, while its lateral and cornering stiffness are substantially higher, irrespective of the spokes’ configurations considered. The considerably higher cornering stiffness of the NPW designs may cause rapid saturation of the cornering force under very low side slip conditions and thus side slippage of the wheel under higher side slip angles. Efficient parametric studies using Taguchi and response surface methodologies are further performed using the verified NPW models so as to investigate the influences of multiple design parameters and the two-factor interactions on their multi-axis and cornering stiffness characteristics as well as natural frequencies of important vibration modes. The natural frequencies are extracted for the stationary NPW with vertically movable spindle and ground contact. The results from the experiment designs are used to develop guidance for design tuning of the NPW in order to achieve desired stiffness and modal properties. The results reveal that the design parameters of the honeycomb NPW can be tuned to achieve significantly lower lateral and cornering stiffness, which are comparable to those of the reference pneumatic tire. These designs, however, in general are coupled with higher thickness of the core layer and tread, which tend to lower the longitudinal stiffness. A novel design concept, called “symmetric helical honeycomb spokes” is subsequently proposed for the NPW. The relative merits of the proposed helical spokes design are evaluated in terms of multi-axis and cornering stiffness properties of the wheel using the verified NPW models by varying the helix angle of the spokes. The results show that introducing the “symmetric helical honeycomb spokes” offer notable reductions in both lateral and cornering stiffness and higher longitudinal stiffness with only slight increase in mass of the NPW.