An analysis is proposed for determining the static and kinematic characteristic lines for a medium of anisotropic cohesive clays. It is proved that, similar to the isotropic case, the velocity field and the stress field coincide and their lines intersect at an angle of π/2. The compatibility equations along the slip lines are derived. An adopted strength function containing four degrees of freedom has proved to be in very satisfactory agreement with laboratory tests. The above derivation is applied to determination of the bearing capacity. It is shown that for a considerable amount of anisotropy, a misleading evaluation of the bearing capacity may be reached if the anisotropic phenomenon is disregarded.