Dynamic complex heat and water transport in building constructions can be calculated using modern simulation software such as Wufi, Delphin, Math, Comsol Multiphysics and other. This software is suitable for the evaluation of the thermal and hygric processes in constructions of historical buildings. Because it includes many important factors such as dynamic boundary conditions, solar radiation, driven rain, ground water, diffusion and others. The heat and water transport parameters of historical materials are needed for simulation of coupled heat and water transport in building materials. The Kežmarok sandstone was chosen for analysis. One of the important material parameters for evaluation of complex heat and water transport in building constructions are water vapor transmission parameters. Vapor transport can be described as water vapor diffusion resistance factor, water vapor diffusion coefficient and diffusion equivalent air layer thickness. The dry cup and wet cup method were used to determine the water vapor transmission parameters of Kežmarok sandstone.