The deep learning community has recently shifted its focus from designing proteins to nucleic acids like RNA. However, the structure-based design of RNA-based biomedicine is limited by de novo RNA backbone generation, which opens doors to early intervention of diseases and signalling for cell-level activity. In this thesis, we develop a generative model based on the recent conditional flow matching framework to design novel RNA backbones starting from random noise. We represent RNA backbones as a point cloud of rigid-body frames that are iteratively denoised. Our in silico evaluation demonstrates our method can design realistic RNA backbones and retrieve the naturally occurring distributions of local structural measurements, with fast sampling speeds of ~4 seconds per backbone. We also report 43.3% of our samples being designable, ie, there exists a nucleotide sequence that folds into the generated backbone. This is the first work on RNA backbone design, and we have established fundamental protocols for backbone modelling and evaluation.