Transient simulation programs, either nodal analysis-based electromagnetic transient program (EMTP-like) or state-variable-based, are used very extensively for modeling and simulation of various power and energy systems with electrical machines. It has been shown in the literature that the method of interfacing machine models with the external electrical network plays an important role in numerical accuracy and computational performance of the overall simulation. This paper considers the state-variable-based simulation packages, and provides a constant-parameter decoupled RL-branch equivalent circuit for interfacing the ac induction and synchronous machine models with the external electrical network. The proposed interfacing circuit is based on the voltage-behind-reactance formulation which has been shown to have advantageous properties. For the synchronous machines, this paper describes both implicit and explicit (approximate) interfacing methods. The presented case studies demonstrate the advantages of using the proposed interfacing method over the traditional qd-models that are conventionally used in many simulation packages.