Non-pneumatic tyres have been developed and are being investigated, but are not very prevalent. Many design studies are still needed from the viewpoint of material, pattern, and structures. However, no systematic research for such important design issues has been reported in the literature up to now. In this article, topology optimization was utilized to determine optimal topological patterns of non-pneumatic tyres in the design process, with the goal of matching the static stiffness of the current pneumatic tyres. Under this optimization formulation with weighted compliance and a volume constraint, several different patterns were obtained depending on the number of sections, volume fraction, and weighting factors. Among them, three representative patterns were chosen and analysed for possible applications under working conditions. This article proposes a systematic and efficient tool for designing the topological patterns of non-pneumatic tyres.