By　modifying　the　spatial　distribution　of　constituent　material　phases,　phononic　crystals　(PnCs)　can　be　designed　to　exhibit　band　gaps　within　which　sound　and　vibration　cannot　propagate.　In　this　paper,　the　developed　topology　optimization　method　(TOM),　based　on　genetic　algorithms　(GAs)　and　the　finite　element　method　(FEM),　is　proposed　to　design　two-dimensional　(2D)　solid　PnC　structures　composed　of　two　contrasting　elastic　materials.　The　PnCs　have　the　lowest　order　band　gap　that　is　the　third　band　gap　for　the　coupled　mode,　the　first　band　gap　for　the　shear　mode　or　the　XY34Z　band　gap　for　the　mixed　mode.　Moreover,　the　effects　of　the　ratios　of　contrasting　material　properties　on　the　optimal　layout　of　unit　cells　and　the　corresponding　phononic　band　gaps　(PBGs)　are　investigated.　The　results　indicate　that　the　topology　of　the　optimal　PnCs　and　corresponding　band　gaps　varies　with　the　change　of　material　contrasts.　The　law　can　be　used　for　the　rapid　design　of　desired　PnC　structures.