Multiwire cable bundles located inside electrically large objects play a crucial role in ensuring their electromagnetic safety. The cable bundles are seldom parallel to the Cartesian coordinates and, hence, they are difficult to handle by using the finite-difference time-domain (FDTD) algorithm. Our motivation in this article is to develop an efficient time-domain field-to-wire coupling model for obliquely oriented multiwire cables with junctions, based on the multiconductor transmission line theory. The multiconductor transmission line equations are discretized by using the 1-D FDTD method. The distributed sources on the cables are obtained by adopting an interpolation technique. The junctions are handled by making use of three theorems. The per-unit-length parameters are extracted by solving an electric field integral equation using the 2-D method of moments. The proposed model has been incorporated into the 3-D full-wave in-house solver J Electromagnetic Solver-FDTD (JEMS-FDTD) to efficiently model the induced effects on the cable bundles located inside electrically large objects illuminated by an external electromagnetic field. To validate the accuracy of the algorithm, the induced currents on a five-wire cable bundle are derived and compared with those obtained from a commercial software. Additionally, the proposed methodology is applied to simulate the induced currents on a seven-wire cable bundle inside a vehicle illuminated by a plane wave.