In manifolds of special holonomy, it is interesting to study calibrated submanifolds, which are volume minimizer in their homology classes. We study the calibrated submanifolds in several model spaces of manifolds of special holonomy. These model spaces are all total spaces of some vector bundles, and the zero section is a calibrated submanifold. We show that the zero section is dynamically stable under the mean curvature flow. This is a joint work with Mu-Tao Wang.