The plastic behavior of the material is explained by the movement of dislocations. Better knowledge of defect dynamics contributes to a more complete understanding of plasticity theory. Using Cartan's structural equations and the apparatus of external differential forms, and Yang-Mills' gauge theory and the phenomenology of dislocations and disclinations in solid bodies, the defect field equations were obtained. The theory of elasticity was taken as the starting model. Dislocations, i.e. disclinations, are the result of breaking symmetry in relation to translation, i.e. rotation, respectively. Yang-Mills compensating fields describe the density of defects. The Lagrange function was formed using the minimum coupling principle, then the Euler-Lagrange equations were obtained as field equations by applying calculus of variations. Using Lagrange's function, tensors of energy and moments can be written, as well as the forces of mutual friction of continuum, dislocation, disclination. The integrability conditions of dislocation and disclination equations give the laws of conservation of linear and angular momentum.