Within the framework of classical gauge field theory we present the Cosserat model of a surface described by two-dimensional gauge continuum with T(3) right-pointing open triangle SO(3) symmetry group. The essential result of this paper is the identification of several basic objects of gauge theory, such as the pure gauge potential, the strength field tensor and the Yang-Mills equations with the basic objects of the Cosserat surface theory. This allows to derive several new results both within the Cosserat surface theory and the gauge field theory itself.