Low-cost transporting vehicles are a crucial routine for orchards in the mountainous place. As the core component of the mountainous orchard carrier, the wire rope is easily damaged due to frequent handling of agricultural materials. The mechanical model of carrier wire rope is the prerequisite for studying its damage mechanism. This paper first analyzes the load-bearing characteristics of the wire rope of the carrier and then uses the theory of differential geometry and the elasticity of the wire rope to establish the mechanical model of the wire rope side strand strain ε0 and the axial load T of the wire rope end face in the erect state and the radial contact pressure Fa of the wire rope at the bending section and the mechanical model of the axial tension F and the pulley diameter D of the wire rope end face. On the basis of the mechanical model and the wire rope geometric solid model, the finite element stress analysis of the wire rope in the vertical state was carried out to verify the accuracy of the wire rope stress model. The results show that when the wire rope was in the vertical state, the wire-wire contact stress was linear directly proportional to the load on the end face of the wire rope; the wire-wire contact stress between the strands was about 12 times that within the strand; the average error between the simulated value and calculated value was about 13.6%, proving the correctness of the established wire mechanics model. When the rope and wheel were in contact, the contact pressure of the outer wire of the side strand was only related to the axial tension of the wire rope end face and the diameter of the pulley but not to the elasticity modulus of the pulley.