  The paper considers the formulation of higher-order continuum mechanics on
differentiable manifolds devoid of any metric or parallelism structure. For
generalized velocities modeled as sections of some vector bundle, a variational
kth order hyper-stress is an object that acts on jets of generalized velocities
to produce power densities. The traction hyper-stress is introduced as an
object that induces hyper-traction fields on the boundaries of subbodies.
Additional aspects of multilinear algebra relevant to the analysis of these
objects are reviewed.
