The paper extends the analytical results obtained by Hwung et al. (1981) and further considers the non-linearity of waves to investigate variation horizontal velocity, temperature distribution induced by interaction of 2-D plane jet and waves. On the steady state, the nonlinear wave is considered as external force in motion equations, the property of momentum conservation of jet flow, and radiation stress are applied to analyze the interaction of waves- jet flow in arbitrary profile. The scale function 1 £` £\1(x) , 2 2£` £\ (x) between the variation function f (x,y) and velocity distribution can also be obtained. The non-dimensional theoretical solution is also useful to estimate the relative characteristics in the physical field. The momentum equation and velocity distribution of interaction without property of temperature diffusion are employed to find the temperature distribution for arbitrary sections. Based on the experiments and theory solution obtained by Hwung et al. (1981) it is found that time-averaged horizontal velocity and temperature are Gaussian distribution, the coefficient of horizontal velocity 1 c , and temperature distribution 2 c are 0.105, 0.148, respectively. In the present, two coefficients considered as non-linearity of waves 1 c = 0.124 and 2 c = 0.152 are determined. In other words, it is shown that exact solution and boundary effect included non-linearity of waves is related to velocity of jet flow, wave periods, relative depth and steepness of waves respectively. Comparing with experiments indicated that the analytical solution of the present for MSE is well confirm the experimental results and better than linear results obtained by Hwung et al. (1981) The influence due to interaction of 2-D turbulent jet flow and Stokes waves can be obtained by using dimension analysis. Moreover, the related properties inside the flow also can be estimated.