The modified (g′/g2)- expansion method for finding traveling wave solutions of nonlinear\nevolution equations is presented in this article, which can be considered as a generalization of\nthe well known (G\n′\nG )-expansion method given recently by M. Wang et al. As applications of\nthis method, we study some nonlinear evolution equations in mathematical physics, namely, the\n(3+1)-dimensional Potential-YTSF equation and the (1+1)-dimensional Vakhnenko equation.\nWith this method, general types of soliton solutions, periodic solutions and rational solutions\nfor these nonlinear evolution equations are obtained.