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In this work, we construct closed form traveling wave solutions to some nonlinear evolution equations (NLEEs) associated with mathematical physics. This work implements the well-established generalized Kudryashov method (gKM) to compute new closed form traveling wave solutions to the Burgers-Huxley equation, the mKdV equation and the first extended fifth order nonlinear equation. Furthermore, in this investigation, we discuss the achieved results in details and portrayed some 2D and 3D figures with the aid of symbolic computation package like Mathematica. The worked-out results ascertained that the suggested generalized form of the Kudryashov method is a simple, efficient and reliable technique to deal with other kinds of NLEEs.