We derive and numerically demonstrate that perfect absorption of elastic waves can be achieved in two types of ultra-thin elastic meta-films: one requires a large value of almost pure imaginary effective mass density and a free space boundary, while the other requires a small value of almost pure imaginary effective modulus and a hard wall boundary. When the pure imaginary density or modulus exhibits certain frequency dispersions, the perfect absorption effect becomes broadband, even in the low frequency regime. Through a model analysis, we find that such almost pure imaginary effective mass density with required dispersion for perfect absorption can be achieved by elastic metamaterials with large damping. Our work provides a feasible approach to realize broadband perfect absorption of elastic waves in ultra-thin films.