Rational design theories for highway and airport pavements are presented together with an invention of a much superior paving material, comprising recycled Ethylene Vinyl Acetate (EVA) mixed and compacted with graded aggregates. EVA is the binder (cheaper than asphalt), and the new paving material, called EVAPAVE, is four times stronger and tougher than asphalt concrete, and twice as strong and tough as high quality cement concrete. Fracture mechanics is used for determining the fatigue life of the pavement AC surface, while the stress-dilatancy theory is used for the rutting of the pavement. The theories are then combined to obtain the interaction of fatigue and rutting. Several examples are presented to illustrate the design methodology. The new pavement will not require joints and will not have bumps or depressions and will be the smoothest riding pavement, with huge savings in construction and maintenance and in vehicular fuel and maintenance costs, estimated to exceed $10 billion per year in the U.S. alone. Its fatigue life will outlast any other pavement by more than seven times.