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This paper is concerned with modeling computer experiments with multiple responses. It has been common that one may collect multiple responses from a physical or computer experiment. However, to our best knowledge, there is little work to model computer experiment with multiple responses. In this paper, we propose a modeling procedure for such computer experiment by using a multivarate kriging model, a natural extension of the ordinary kriging model. We further extend functional ANOVA of single response to multiple response and apply it for analyzing the effect of each design variable. The proposed methodology is demonstrated by an analysis of data collected from a case study concerned with the design of the engine structure to minimize the radiated noise.