A strand or cable consists of a central core surrounded by a number of wires wound helically in a single layer or multilayers. There are three modes of contact in a simple straight strand. The first type is a core-wire contact in which the wires in the layer are in contact with the core only. In the second type, the wires in the layer are in contact among themselves and not with the core, while in the third type there is a coupled contact among the core and all the wires. Most literature handled the cable assembly with either the core-wire or the wire-wire contact because of the simplicity of the loads acting in these distinct contact modes. An attempt is made in this paper to model the strand with a coupled core-wire and wire-wire contact and deduce its equations of equilibrium. The numerical analyses of strand force, twisting moment, strand stiffness, contact force, and contact stress are carried out based on the equilibrium of thin rods and the results are compared with earlier research works. The importance of the inclusion of interface forces and their effects is studied.