This paper deals with the experimental and numerical characterization of a high damping CuAlMn sheet with a martensitic micro-structure at ambient temperature. A Cu-Al-Mn shape memory alloy containing 11.65 wt.% of Al and 3 wt.% of Mn, was cast and hot rolled to the thickness of 0.4-0.3 mm. Transformation temperatures, micro-structure and mechanical properties were studied. Effects of the heat treatment on damping were investigated, identifying the proper heat treatment to obtain a higher damping. Having to model the amplitude dependent damping of the material investigated, a material model was developed based of cyclic behavior under traction-compression load. The model was validated with experiments on the non-linear damping of the material.