The CALorimetric Electron Telescope (CALET) has been measuring high-energy cosmic rays on the International Space Station since October 2015. One of the scientific objectives is the precise measurements of the boron-to-carbon flux ratio and the energy spectra of nuclei to investigate the cosmic-ray acceleration and propagation in the Galaxy. The instrument has capabilities to identify individual nuclei elements up through Iron with excellent charge resolution and cover the wide energy range from 10 GeV to a PeV. In this paper, we will present the details about the analysis of nuclei measurements and preliminary results of boron-to-carbon flux ratio and energy spectra of heavy nuclei components up to Iron based on three years of operations.