Abstract: This paper studies the model-robust design problem for response surface in R^s by applying the reproducing kernel Hilbert space approach. We assume that the model bias includes the effects due to higher degree terms of multivariate Hermite polynomials. If bias is severe, the design points should be pulled in towards the origin, while if bias is minimal, the design points should be spread out slightly. The designs are invariant with respect to orthogonal transformations and robust against the vary of bias over some range.