A topological index is a numerical quantity correlating an important physicochemical property of a chemical compound. Study of such indices has found important and vital applications in QSAR/QSPR study, drug design, and pharmacology. In this paper, we use a novel mathematical method of edge partition to compute the Wiener polarity index and a special cases of generalized Wiener polarity index of boron-triangular and boron-α nanotubes. Furthermore, we compute certain distance-based indices of boron triangular nanotubes by using the edge partition technology. A computational analysis and graphical comparison of computed indices is also given to confirm the validity of obtained results.