  This paper is motivated by recent developments of higher gauge theory.
Different from its style of using higher category theory, we try to describe
the concept of higher parallel transport within setting of classical principal
bundle theory. From this perspective, we obtain a global geometric proof on a
generalized 3-dimensional non-abelian Stokes' theorem related to parallel
transport on surfaces. It can be naturally extended to four dimension when the
underlying crossed module is replaced by crossed 2-module. This 4-dimensional
Stokes' theorem yields a global formula for volume holonomy, and also
guarantees its gauge invariance. In the process, we also find composition
formulas for parallel transport on volumes which have been seen in the case of
surfaces.
