In this paper we consider a generalized double dispersion equation of Porubov’s type<sup>4,5</sup>. which describes the propagation of the longitudinal strain waves in the rod. By analogy with the optical case<sup>2</sup>, 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 authors<sup>4,5</sup>. It will be shown that our analytical solutions describe very well the results obtained by numerical simulations<sup>6</sup>.