Abstract: Numerical integration is of great importance in a numerical analysis. With the reference to Chebyshev's equal weight quadrature, a modified Chebyshev quadrature is proposed after incorporating the end points of an interval. The practical application of Chebyshev's equal weight quadrature is restrictive since the order of quadrature with mere real abscissas cannot exceed nine. The modified Chebyshev quadrature alleviates the restriction considerably and renders it applicable in a weak-form quadrature element analysis. It is applied to the evaluation of integrals and linear and non-linear weak form quadrature element analysis of rods and beams. Results are compared with analytical solutions and those obtained using Lobatto quadrature, verifying the accuracy and the effectiveness of the proposed quadrature.