In this paper we briefly review the latest progress on the propagation of stress in granular bed and the resistant force of an object moving in granular media, and report our studies on the grain-size effect, which revals the discrete properties of granular media. We found that the sinking depth of a sphere on a granular bed driven by its own weight decreases monotonically with increasing grain-size. The supporting force of the granular bed experienced by the intruder sphere, during sinking, is measured. It is found that except for about 1 mm depth near the surface, the supporting force and the sinking depth of the sphere is related by a power-law with exponents between 1.5—1.0. The exponent decreases with increasing grain-size. This-size dependence of the power-law relation can be a macroscopic manifest of the reorganization of the stress chains in the granular system during the sinking process of the intruder sphere.