The problem of determining the bearing capacity of a strip footing resting on the surface of a homogeneous half space and subjected to an inclined, eccentric load, is solved within the framework of the yield design theory assuming that the soil is purely cohesive without tensile strength according to Tresca's strength criterion with a tension cut-off. The soil foundation interface is also purely cohesive, in terms of the homologous strength criterion with a tension cut-off. As in a companion paper [Salencon & Pecker, 1995], both the static and the kinematic approaches of the yield design theory are used. New stress fields are constructed, in order to comply with the condition of a tension cut-off within the soil medium, and new lower bounds are determined as substitutes to those given in the companion paper. Velocity fields taking advantage of the tension cut-off contribution in the expression of the maximum resisting work are also implemented, giving new lower bounds. As may be expected from common sense and from the general results of the theory, it appears that the tension cut-off condition within the soil medium results in lower values of the bearing capacity of the foundation, and that the gravity forces acting in the soil mass have a stabilizing effect.