A non-pneumatic mechanical elastic tire (ME wheel) was introduced, and the grounding characteristics of the ME wheel under a rolling condition with a camber angle were investigated with the combination of finite element simulation and experimental research. According to the ME wheel structure and material characteristics, a numerical simulation model of the ME wheel was established using the finite element (FE) method. The stiffness tests were carried out to verify the accuracy of the simulation model of the ME wheel. To highlight the advantages of the ME wheel, an inflatable tire was selected as the reference tire, and the grounding characteristics of these two tires with different camber angles were compared and analysed in free rolling, braking, and driving conditions. Different slip ratio values for the ME wheel and inflatable tire were applied in driving conditions to analyse the influence of the slip ratio on the grounding characteristics. The obtained results indicated that both the ME wheel and inflatable tire will gradually suffer partial wear of the tread surface as the camber angle increases, but the pressure concentration of the inflatable tire is more serious. The research can provide a basis for structural optimization and comprehensive mechanical performance analysis of the ME wheel.