Exact gation in relaxing solvability for the third order nonlinear evolution media and longitudinal wave propagation with considered. With the aid of symbolic computation equation which describes acoustic wave propa- transverse shearing in nonlinear elastic bar is of computer algebra, abundant explicit exact particular solu- tions to the equation are obtained by using the first integral method. These solutions include the solitary wave so- lutions of rational function, the solitary wave solutions of kink-shape, singular traveling wave solutions, and the periodic wave solutions of triangle function. Some known results are extended and complemented.%研究了模拟松驰介质中声波传播和非线性弹性杆中具横向剪切的纵波传播的一个三阶非线性发展方程的精确可解性．借助计算机代数符号计算Maple，利用首次积分的方法，获得了这个方程的丰富的显式精确解，包括有理分式解，扭状孤立波解，奇异行波解和三角函数周期波解，推广补充了已有结果．
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