A major concern when installing the cables into the underground conduit is minimizing the tensile forces exerted on the cables as they are pulled. This knowledge makes it possible to avoid over conservative design practices and to achieve substantial saving during construction. A general computing algorithm of predicting the tensile force of the cable pulled through the underground conduit with an arbitrary configuration is presented in this paper, which is based on multibody system dynamic formulation. The presented multibody dynamic model for this problem consists of the cable, the underground conduit, and the interaction between the cable and the conduit. In this paper, the cable is modeled by the finite cable element based on an absolute nodal coordinate formulation. The interaction between the cable and the underground conduit is described by the Hertz contact theory. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method for estimating the cable tension.