  We investigate the dispersion properties of the acoustic surface waves on
surface of elastic metamaterials. With an analytical approach, we show that
unconventional acoustic surface waves, with dispersion behaviors very similar
to the electromagnetic surface plasmon polaritons (SPPs) on metal surfaces, can
exist on the elastic metamaterials around the frequency at which the elastic
Lam\'e's constants satisfy lambda+mu=0. Two typical elastic metamaterials are
exemplified to demonstrate such peculiar acoustic surface waves.
