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Model management is the key for surrogate-assisted evolutionary algorithms to provide high-quality solutions for computationally expensive optimization problems. In this paper, a surrogate-assisted evolutionary algorithm based on radial space division is proposed for expensive many-objective optimization problems. The algorithm projects the individuals in the high-dimensional space to the radial space. Then, the location distribution of the individuals in the radial space and the uncertain information provided by the Kriging model are used for managing the surrogate model. In addition, two archives are used to manage the model, a fixed archive is used to hold the data that builds the Kriging model, and a variable archive is used to save the non-dominant solution. Finally, the performance of the proposed algorithm is tested on three sets of benchmark problems and two automobile structure design problem. The simulation results show that the algorithm is more competitive than the commonly used surrogate-assisted evolutionary algorithms. • A surrogate-assisted evolutionary algorithm based on radial space division is proposed. • Judge the quality of surrogate model by using crowdedness of population in radial space. • The two archives strategy is proposed for the management surrogate model. [ABSTRACT FROM AUTHOR]