Properly modeling the cyclic elastoplastic behavior of structural steels is essential for establishing accurate analyses of structures subjected to earthquake excitation. However, identifying the underlying parameters to simulate such behavior is commonly hindered by the computational burden of carrying out many nonlinear analyses. This work proposes using Bayesian optimization (BO) for solving an inverse problem by which certain parameters for the nonlinear combined isotropic/kinematic hardening model are inferred from cyclic responses of a specimen or a structural component. BO minimizes an error function that represents the difference between the simulated responses and those measured experimentally while providing a global optimization framework for parameter identification, reducing the number of simulations, and addressing observational noise. It is found that BO has higher robustness as compared with some population-based optimization algorithms when expending the same number of simulations. Identification results for a specimen and a cantilever show a good ability of identified parameters to capture the behavior of structural steels under different cyclic loadings. They also suggest a possibility of identifying the parameters for multiple materials from cyclic tests of a structural component that is remarkable because cyclic material tests are difficult and usually not carried out before structural tests. Experimental measures from various loading histories should be simultaneously used for identification as they can mitigate the bias toward a specific loading history, which may lead the parameters to inaccurate prediction of material behavior under other loading histories.