By means of computerized symbolic computation and a modified extended tanh-function method for constructing multiple traveling wave solutions of nonlinear physical equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear equations of special interest in physics namely, the Broer-Kaup-Kupershmidt, nonlinear coupled plasma, and coupled-nonlinear reaction-diffusion equations. As a results, we can successfully recover the previously known solitary wave solutions that had been found by other sophisticated methods. The method is straightforward and concise, and it can also be applied to other nonlinear equations in physics.