  For high-order continuum mechanics and classical field theories
configurations are modeled as sections of general fiber bundles and generalized
velocities are modeled as variations thereof. Smooth stress fields are
considered and it is shown that three distinct mathematical stress objects play
the roles of the traditional stress tensor of continuum mechanics in Euclidean
spaces. These objects are referred to as the variational hyper-stress, the
traction hyper-stress and the non-holonomic stress. The properties of these
three stress objects and the relations between them are studied.
