In this work, using a two‐dimensional particle‐in‐cell Monte Carlo collision computation method, terahertz (THz) radiation generation via the interaction of two‐colour, ultra‐short, high‐power laser pulses with the polyatomic molecular gases sulphur dioxide (SO2) and ammonia (NH3) is examined. The influence of SO2 and NH3 pressures and two‐colour laser pulse parameters, i.e., pulse shape, pulse duration, and beam waist, on the THz radiation generation is studied. It is shown that the THz signal generation from SO2 and NH3 increases with the background gas pressure. It is seen that the THz emission intensity for both gases at higher laser pulse durations is higher. Moreover, for these polyatomic gases, the plasma current density increases with increase in the laser pulse beam waist. A more powerful THz radiation intensity with a larger time to peak of the plasma current density is observed for SO2 compared to NH3. In addition, many THz signals with small intensities are observed for both polyatomic gases. It is seen that for both SO2 and NH3 the generated THz spectral intensity is higher at higher gas pressures.