The differentialalgebraic equations are often chosen as the mathematical models of the dynamics of multibody systems in order to achieve the numerical emulation for the multibody systems. Based on the existing constraint violation stabilization method, a modified numerical method for the equations with singularity positions is proposed in the present paper. By correcting the violation of the velocity and controlling the stability term in the modified method, the differentialalgebraic equations with singularity positions are solved, and the values of the coefficients in the stability term are suggested. Thus,the numerical difficulty, due to the singularity of the multibody systems,is effectively eliminated. The contrast between the numerical results of the example using the modified method and the ADAMS soft demonstrates the effectiveness of the proposed modified method. The balance based on the law of conservation of energy also proves the effectiveness of the method.