An elastic water-permeable polymeric concrete composition, a formulation method therefor, an elastic water-permeable polymeric concrete structure using the composition, and a method for constructing the structure. The polymeric concrete composition is formulated by integrating a rubber powder ground from waste tires or waste rubber and an aggregate using a polymeric binder, and if required, by adding a pigment and aromatic capsules capable of providing remedial and psychological effects. The polymeric concrete structure manufactured using such polymeric concrete composition has appropriate elasticity, water permeability, strength and a pleasant aroma. Thus, the polymeric concrete composition is useful for paving a footpath, a roadway, a bikeway, a railway crossing, a parking lot, a stadium, a racing track, a landing strip, etc., and as a material for civil engineering and constructions such as blocks, tile sound-absorbing plates, soundproofing plates, soundproofing walls and retaining walls.