The detailed map of the groundwater discharge on a tunnel wall must be a useful information to evaluate the groundwater flow in rock mass. A technique of the evaporation measurement that was newly developed by the present authors seems to be an effective tool to accurately measure the small value of the discharge of water coming from a low permeable rock mass. The vapor flux that is mainly transported by the molecular diffusion in the laminar flow layer formed just near the wall is measured by using two couples of humidity and temperature sensors. The applicability of the technique and some characteristic features of the vapor flow in the vicinity of the wall, i. e., the thickness of the laminar layer and the vapor flow from a high permeable fracture are theoretically as well as experimentally studied. It is found that the technique is highly practical.