Metamaterials can exhibit electromagnetic and elastic characteristics beyond those found in nature. In this work, we present a design of elastic metamaterial that exhibits multiple resonances in its building blocks. Band structure calculations show two negative dispersion bands, of which one supports only compressional waves and thereby blurs the distinction between a fluid and a solid over a finite frequency regime, whereas the other displays 'super anisotropy' in which compressional waves and shear waves can propagate only along different directions. Such unusual characteristics, well explained by the effective medium theory, have no comparable analogue in conventional solids and may lead to novel applications.