  We present a study of elastic metamaterial that possesses multiple local
resonances. We demonstrated that the elastic metamaterial can have
simultaneously three negative effective parameters, i.e., negative effective
mass, effective bulk modulus and effective shear modulus at a certain frequency
range. Through the analysis of the resonant field, it has been elucidated that
the three negative parameters are induced by dipolar, monopolar and quadrupolar
resonance respectively. The dipolar and monopolar resonances result into the
negative band for longitudinal waves, while the dipolar and quadrupolar
resonances cause the negative band for transverse waves. The two bands have an
overlapping frequency regime. A simultaneously negative refraction for both
longitudinal waves and transverse waves has been demonstrated in the system.
