Stress tensors are used in strength analysis of structures, fluid dynamics, electromagnetism, and general relativity. Yet, from the theoretical point of view, the stress tensor object is not a primitive one. It is derived on the basis of some physically motivated mathematical assumptions. Following a short introduction to the fundamentals of the classical theory, we will present a formulation of stress theory on general differentiable manifolds, devoid of any particular Riemannian metric. The basic mathematical object is the configuration space---the Banach manifold of k-times continuously differentiable sections of a fiber bundle over a compact base manifold---the material body. The choice of topology is natural so that the set of embeddings of the body manifold in a space manifold is open in the manifold of all mappings. Forces are defined to be elements of the cotangent bundle of the configuration space and their action on virtual velocities---elements of the tangent bundle---is interpreted physically as virtual power. Stresses and hyper-stresses emerge naturally from a representation theorem as measures, valued in the dual bundles of some jet bundles, which represent forces.