When structure using energy dissipating device suffers from earthquake, its core materials will first go into the plastic yield stage and consume earthquake input energy by hysteretic deformation to protect the main structure. Therefore, the numerical simulation of core materials constitutive relation is the basis of seismic analysis and design with dissipation device. Theconstitutive relation of energy dissipation device under monotonic loading and cyclic loading elastic-plastic seismic response of the structure with energy dissipation device were investigated in the numerical simulation of monotonic constitutive relation, cyclic constitutive relation and skeleton curve of SN490B steel. The simulations include the four stages which are elastic stage, collapse stage, strain-hardening stage and secondary flow plastic stage of core material using Esmaeily-Xiao secondary flow plasticity model; the constitutive response of core materials under cyclic loading using combined hardening; the skeleton curve using the Ramberg-Osgood model, dimensionless Ramberg-Osgood skeleton curve model and double-linear model. Based on finite element software ABAQUS combined with numerical simulation parameters, numerical simulation of 16 different cyclic loading tests was conducted and compared with the test results. The results show that: mathematical model can be used to simulate the monotonic constitutive response, cyclic constitutive response and cyclic skeleton curve of SN490B steel accurately. Numerical simulation and experimental results fit well.