SUMMARYThis work extends the application of the generalized di erential quadrature rule (GDQR) to an eighthorder boundary-value di erential equation with four boundary conditions at boundaries. The di erential quadrature expression and explicit weighting coe cients for the eighth-order di erential equation are formulated for a ÿrst time to implement the GDQR more accurately. A circular cylindrical single-barrel roof is employed as an example. The numerical results show good accuracy and convergence with only a few sampling points. The application of the GDQR is straightforward and has clear advantages in the implementation of multiple boundary conditions over the existing -point technique. The GDQR has demonstrated itself as a general numerical method to solve high-order di erential equation with multiple boundary conditions.