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Two-dimensional phononic crystals (PC) with square or triangular lattices composed of steel rods in a polymer matrix are studied. The band structure of the PC exhibits several negative branches. Among them, one allows the negative refraction of longitudinal waves transmitted through the PC. The left-handed behaviour of the PC is exhibited numerically as well as experimentally, by using a prism shaped PC. Finally, a numerical simulation is presented, with the PC immersed in a fluid, for focusing applications.