The transmission of one-hundred-femtosecond-long pulses by following an on-off keying modulation spread in time has been recently proposed as a way to enable Terahertz (THz)-band (0.1-10 THz) communications over short distances. The transmission of ultra-short pulses minimizes the probability of collisions due to the very small time that the channel is occupied by each user. However, given that many of the envisioned applications of THz-band communications involve very large node densities, multi-user interference results unavoidably. In this paper, a stochastic model of multi-user interference is developed and experimentally validated. The model takes into account the fact that the interference power at the receiver is not a combination of the received powers from the individual nodes, rather the power of the combination of the signal amplitudes. For this, first, the probability density function (PDF) of the interference generated by one interfering node at the receiver is obtained starting from the PDFs of the pulse received energy and the PDF of the pulse shape. Then, the model is extended to account for multiple nodes which can constructively or destructively interfere. Finally, the developed model is experimentally validated and numerical results are provided.