A novel numerical model for seismic damage analysis of inelastic two degree of freedom (2DOF) system under bi directional excitations was developed by taking the strength degradation, stiffness deterioration and pinching effect into account. The influences of bidirectional excitations, strength degradation, stiffness deterioration and pinching effect on statistical characteristics of seismic damage index of inelastic 2DOF system were investigated using 69 selected earthquake records. The results show that seismic damage index of inelastic 2DOF system can be described as either the Lognormal or the Frechet distribution variable; the seismic damage index of inelastic 2DOF system can be approximated by the square root of sum of square (SRSS) of seismic damage index of single degree of freedom (SDOF) system; an decrease in post yielding stiffness or consideration of strength degradation, stiffness deterioration and pinching effect may increase the seismic damage index remarkably.