AbstractA localized triangular differential quadrature method is introduced in this article. Not only is the existing limitation on the approximation order in the triangular differential quadrature eliminated but also the convergent rate is enhanced in the new method. As an example to validate the new method, elastic torsion of prismatic shaft with regular polygonal cross section is studied and excellent agreement with available theoretical and analytic solutions is reached. It is believed that the present work further widens the applicability of the triangular differential quadrature technique. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 682–692, 2003