In a recent work, a proximity- and skin-effect aware formulation known as the surface-volume-surface electric field integral equation discretized with 2-D method-of-moments (MoM) was optimized to efficiently extract the frequency dependent series impedance matrix of cables with arbitrary shapes. However, it was only applied to sector-shaped and coaxial cables due to the constraints on computing the shunt admittance matrix using closed-form approximations. This work presents formulation, discretization, and optimization techniques, for fast computation of the shunt admittance matrix of arbitrary-shaped cables by discretizing the problem of the quasi-electrostatics using 2-D MoM. With the proposed MoM techniques and optimization strategies, it is possible to accurately compute all the electrical parameters of arbitrary-shaped cables required in electromagnetic transient programs (EMTP) using today’s typical computer power and with reasonable computational times. This provides an efficient modeling tool for any desired cable design. Frequency domain solutions of the proposed technique are compared against the finite-element method as well as the classical approximate formulas available for pertinent cable models. The resulting time domain transient simulations in EMTP are also investigated.