This work presents a theoretical and experimental characterization of shape memory alloy metal rubber (SMA-MR) material. SMA-MR is a novel porous damping solid made of coil entangled nitinol wires. The constitutive model proposed in this work takes into account the geometry of the coils used, the manufacturing parameters of the SMA-MR material together with the thermo-mechanical behavior of the shape memory alloy wires. Metal rubber samples made with nitinol constitutive material are fabricated and tested under different quasi-static loading and temperature conditions. The special characteristics of SMA-MR such as hysteretic behavior, nonlinear stiffness, transverse isotropy, dry friction damping property and temperature dependency are predicted by the model, with the comparison between the theoretical and experimental results yielding discrepancies lower than 5% in the majority of the conditions considered.