Effects of simultaneous, together with separate addition of hydrogen to the fuel and water vapour to the oxidizer on soot formation in laminar, counterflow ethylene diffusion flames at atmospheric pressure were studied numerically. A polycyclic aromatic hydrocarbon (PAH)-based sectional soot model coupled with detailed gas-phase chemistry, was used to investigate the underlying chemical pathways of soot formation. In agreement to available studies, the results showed that, in addition to the dilution effects, the fuel-side enrichment of hydrogen and/or oxidizer side dilution of water vapour suppress the soot formation through chemical effects. The reduction in soot formation through chemical effects of H2 and H2O addition is mainly attributed to the reduced rates of soot surface growth due to suppression of the H-abstraction reaction in the hydrogen-abstraction-C2H2-addition (HACA) sequence as a result of an increased molecular hydrogen concentration. The simulations indicate that the chemical effects tend to increase PAH concentration within the soot formation region, which results in increased soot nucleation rates and number density. However, the contribution of soot nucleation in the overall soot formation process becomes secondary, while the soot surface growth predominantly governs the chemically inhibiting effects of H2 and H2O addition. Compared to separate addition, simultaneous addition of hydrogen to the fuel and water vapour to the oxidizer proves to be more effective in soot suppression for the same dilution level, since there exist weak synergistic effects between H2 and H2O. The numerical analysis further demonstrates that the separate, as well as simultaneous addition of H2 and H2O, tend to decrease the number density of larger-sized particles, causing the reduction in average soot particle size.