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Abstract.We study the pointwise estimates of solutions for two-dimensional viscous shallow water equations.The main approach in this paper is based on the detailed analysis of Greens function for the linearized system.We decompose the Greens function into three parts: lower frequency part, middle part and higher frequency part.Then by means of Taylor expansion,Fourier analysis and Kirchhoff formulas, we obtain the pointwise estimates of these three parts.Besides the analysis of Greens function, the elaborate analysis of the nonlinear terms is an indispensable part for us due to the fact that the pointwise estimates of the solutions to the nonlinear system are obtained by joining the analysis of the Greens function and the nonlinear terms together.Moreover, the pointwise estimates of the solutions are obtained and shown to exhibit the Huygens principle.