We present a single-phase double-sided pillared metamaterial with effective mass density and elastic modulus simultaneously negative. The negative effective mass density is achieved owing to the combination of the symmetric bending resonance and the antisymmetric compressional resonance of both pillars, whereas the negative effective elastic modulus results from their symmetric compressional resonance. Comparisons with the single-sided pillared structure are made. The dependence of the width of the double-negative band against the geometric parameters of the unit cell is also investigated. In addition, the negative refraction and the zero-index refraction of the symmetric Lamb wave in the deep-subwavelength scale are observed, while at the same frequency, the propagation of the antisymmetric Lamb wave is forbidden.