In this work minimally supported D-optimal designs for response surface models with spatially correlated errors are studied. The spatially correlated errors describe the correlation between two measurements depending on their distance d through the covariance function C(d)=exp(-rd). In one dimensional design space, the minimally supported D-optimal designs for polynomial models with spatially correlated errors include two end points and are symmetric to the center of the design region. Exact solutions for simple linear and quadratic regression models are presented. For models with third or higher order, numerical solutions are given. While in two dimensional design space, the minimally supported D-optimal designs are invariant under translation¡Brotation and reflection. Numerical results show that a regular triangle on the experimental region of a circle is a minimally supported D-optimal design for the first-order response surface model.