Abstract: The wavelet-DQ method combines the classic differential quadrature (DQ) method, the multi-resolution analysis theory, and a constructor of scaling function-basedinterpolation base functions.This is a new method for solving boundary valueproblems of differential equations. This method is applied to analyze the longitudinal vibration of an elastic straight rod with variable cross-section, to obtain thefrequency equation. With different parameters, the natural frequencies ofclamped-clamped, free-free wedge-shaped straight rod and cone-shapedstraight rod are obtained. Numerical results show that the method is simpleand enjoys high-precision. This method can be applied to othermechanical problems in numerical analysis.