In this paper, the physical approach to model external (air-induced) passive intermodulation (PIM) is presented in a frequency-division duplexing (FDD) multiple-input multiple-output (MIMO) system with an arbitrary number of transceiver chains. The external PIM is a special case of intermodulation distortion (IMD), mainly generated by metallic objects possessing nonlinear properties ("rusty bolt" effect). Typically, such sources are located in the near-field or transition region of the antenna array. PIM products may fall into the receiver band of the FDD system, negatively affecting the uplink signal. In contrast to other works, this one directly simulates the physical external PIM. The system includes models of a point-source external PIM, a finite-length dipole antenna, a MIMO antenna array, and a baseband multicarrier 5G NR OFDM signal. The Channel coefficients method for multi-PIM-source compensation is replicated to verify the proposed external PIM modelling approach. Simulation results of artificially generated PIM cancellation show similar performance as real-life experiments. Therefore, the proposed approach allows testing PIM compensation algorithms on large systems with many antennas and arbitrary array structures. This eliminates the need for experiments with real hardware at the development stage of the PIM cancellation algorithm.