The water diffusivity and the development of swelling pressure are investigated in buffer materials to be used for the geologic disposal of high-level radioactive waste during the stage of unsaturated water uptake. Highly compacted blocks of Japanese Na bentonite and a bentonite-sand mixture are used as the buffer material. The water diffusivity of the blocks has turned out to be approximately equal to that of Wyoming bentonite MX-80. Assuming that the local swelling pressure in a small element of a confined bentonite mass is proportional to the degree of saturation of the local area, an elastic model with an apparent Young's modulus is developed for the first step. According to this model, the swelling pressure of the bentonite mass as a whole is proportional to the avarage degree of saturation of the mass. For the development of the swelling pressure in the blocks, the calculated curve by this model is in good agreement with the experimental results except during the early parts of the process. Key words : bentonite, water uptake, water diffusivity, swelling pressure, elastic model, radioactive waste disposal.