The Hausdorff dimension and packing dimension of the image and graph of Gaussian vector fields and index-$\alpha$ stable fields are obtained under general conditions which allow for different local behavior of the components and for dependence among them. These results correct some error in print. The condition for an indexed-$\alpha$ stable field to have $k$-multiple points are considered and in the case of $Nk > (k - 1)\sum^d_{j=1} \alpha_j$, the Hausdorff dimension of the set of $k$-multiple times is given.