Abstract: This paper deals with Bayesian design in the unit cube for multiresponse prediction with infinite-dimensional random functions as priors. In order to make optimization more tractable, we adopt the asymptotics used in Mitchell et al. (1994). It is shown that the uniform continuous design on the unit cube is optimum under the asymptotic Bayes criterion for a certain prior specification. It follows that the uniform design proposed by Fang and Wang (1994) performs very well for the multiresponse prediction.