This paper explores the optimum design of the power grid. A simplified model of the power grid, based on the assumption of uniform current distribution and some approximations, is presented. This model is shown to give the IR drop at the grid center with error less than 0.1% compared to full simulation. In addition, the optimum sizing of power grid lines for minimum IR drop is derived, based on a general version of the model. Applying the optimum sizing, a uniform grid has the minimum IR drop, for uniform current profile. However, for real chip examples where current profiles are non-uniform, the optimum sizing results in 14% reduction in the IR drop at the center compared to uniform sizing