The Molecular Dynamics technique is used to investigate size segregation by shaking in cohesionless granular materials. Temporal evolution of the height h of the tagged particle with different size and mass is measured for various values of the particle radius and specific gravity. It becomes evident that h approaches the steady state value h∞ independent of initial positions. There exists a threshold of the specific gravity of the particle. Below the threshold, h∞ is an increasing function of the particle size, whereas above it, h∞ decreases with increasing the particle radius. The relaxation time τ towards the steady state is calculated and its dependence on the particle radius and specific gravity is clarified. The pressure gradient of pure systems is also measured and turned out to be almost constant. This suggests that the buoyancy force due to the pressure gradient is not responsible to h∞.