Directional routing of one-way classical wave has raised tremendous interests about spin-related phenomena. This sparks specifically the elastic wave study of pseudo-spin in meta-structures to perform robust manipulations. Unlike pseudo-spin in mathematics, the intrinsic spin angular momentum of elastic wave is predicted quite recently which exhibits selective excitation of unidirectional propagation even in conventional solids. However, due to the challenge of building up chiral elastic sources, the experimental observation of intrinsic spin of elastic wave is still missing. Here, we successfully measure the elastic spin in Rayleigh and Lamb modes by adopting elaborately designed chiral meta-sources that excite locally rotating displacement polarization. We observe the unidirectional routing of chiral elastic waves, characterize the different elastic spins along different directions, and demonstrate the spin-momentum locking in broad frequency ranges. We also find the selective one-way Lamb wave carries opposite elastic spin on two plate surfaces in additional to the source chirality.