Inelastic deformation of gold (Au) atomic cluster is investigated by using molecular dynamics (MD) simulations. We performed compression and unloading tests in which silicon (Si) plates approach each other and push single Au cluster of 4 nm diameter in between. Possibility of super-elastic (hyper-elastic) behavior is discussed in the present study, because the cluster in MD simulation certainly shows large reversible strain in unloading process after compression. The strength of interaction between Si plate and the Au cluster is adjusted to our AFM experiment. Softening in elastic constant by increase of temperature is also discussed.