By means of density functional theory, we systematically investigate the insertion and diffusion of Na and Li in layered Si materials (polysilane and H-passivated silicene), in comparison with bulk Si. It is found that Na binding and mobility can be significantly facilitated in layered Si structures. In contrast to the Si bulk, where Na insertion is energetically unfavorable, Na storage can be achieved in polysilane and silicene. The energy barrier for Na diffusion is reduced from 1.06 eV in the Si bulk to 0.41 eV in polysilane. The improvements in binding energetics and in the activation energy for Na diffusion are attributed to the large surface area and available free volume for the large Na cation. Based on these results, we suggest that polysilane may be a promising anode material for Na-ion and Li-ion batteries with high charge-discharge rates.