Mode superposition method(MSM) is the most commonly used for solving linear response problems of structural dynamics. The major advantage of MSM is that usually a small number of lower mode is sufficient to analysis the response. However, the convergence is slow and many modes would be needed to give an accurate MSM in large structure with many degrees of freedom. The inaccuracies of MSM are caused by mode truncation in the solution. These demerits can be overcome by use of the mode acceleration method(MAM). Example analyses are carried out in simple beam subjected to harmonic loadings and compared the convergence of the joint displacements by the two methods. For relatively low frequency loadings, a good results was obtained by the lowest one mode in MAM, so the method is more economic in numerical analysis on an accurate solution.