In this study, we propose a method for characterizing fluid-mechanical properties of a fluid surface, such as surface dilatational and shear viscosity, by matching the flow visualization and the numerical simulation for a Stokes flow in a three-dimensional cavity. The surface flow is driven by shear stress exerted on the free surface by an external gas flow. The external gas flow is simulated by using a commercial code, while the Stokes flow is calculated by an in-house code. We have found that the surface flow is very sensitive to the surface tension and other properties. The qualitative feature of the surface flow can be reproduced by the parameter tuning.