In this paper we consider a generalized double dispersion equation of Porubov’s type4,5. which describes the propagation of the longitudinal strain waves in the rod. By analogy with the optical case2, the higher orders of nonlinearity have been included which leads to an interesting class of traveling solitary waves for both cases: without cubic nonlinearity and with its presence. The F-expansion method described in3 has been used. As a byproduct, we obtain the results given previously by other authors4,5. It will be shown that our analytical solutions describe very well the results obtained by numerical simulations6.