The paper formulated the theory of the deformation gradient of the first paper in the mechanics of granular materials. Included in this theory are the effects of changes in the zap-volume of the solid part of the observed body as well as first-order deformation gradients. Based on thermodynamic considerations, constitutive equations were derived and the basic equations of motion were obtained and analyzed. The problem of flow of granular materials under the influence of gravity, as well as the influence of the higher-order deformation gradient, was investigated.