In recent years, there has been considerable interest in modelling and simulating interdependencies among critical infrastructures. For most cases, agent-based frameworks are employed for these types of simulation. In this paper, we present a new approach for interdependencies simulation that we have used in the infrastructures interdependencies simulator (I2Sim). I2Sim implementation is based on the matrix partitioning technique named multi-area Thevenin equivalent (MATE). The MATE model has been used for large-scale real-time power system simulation and is an efficient alternative to the existing agent-based critical infrastructure simulation frameworks. Another distinguishing feature of I2Sim is that, it is based on a cell-channel model where interdependencies among different infrastructures can be represented through a formal technique based on the extension of Leontief input-output model. In this paper, we present the implementation architecture of I2Sim. We also discuss some simulation results to show the usefulness of our approach.