Abstract: The main work in this paper is to solve the two-dimensional nonlinear longitudinal wave equation. The perturbation method is used to expand the solution of this equation to the second order with acoustic Mach coefficient. According to the calculation results, the amplitude ratio of the second harmonic propagation components along the x-axis and y-axis to the incident fundamental wave is defined as nonlinear coefficients, and the propagation characteristics of the fundamental wave and the second harmonic are discussed in detail. When the two-dimensional longitudinal wave propagates in a solid, the effects of incident wave frequency, incident angle and sound propagation distance on the nonlinear coefficient are explored. This nonlinear coefficient can describe the propagation regularities of the fundamental wave and the second harmonic of the two-dimensional nonlinear longitudinal wave, and can be used to qualitatively analyze the nonlinearity of solid materials, which provides a theoretical basis for the subsequent exploration of the propagation regularity of oblique incident longitudinal wave in solid.