The capacity of sodium bicarbonate (NaHCO3)s powder to chemically reduce flame speeds and mitigate the effects of accidental explosions is well established. The inhibition of premixed hydrocarbon/air flames by monodisperse (NaHCO3)s solid particles is investigated, here, using theory and numerical simulations. First, an analytical solution for the temperature history of a solid (NaHCO3)s particle crossing a flame shows that the size of the largest (NaHCO3)s particle which can decompose inside the flame front, and act on chemical reactions efficiently, strongly depends on the flame speed. For various fuels and a wide range of equivalence ratios, particles with a strong potential for flame inhibition are identified: hence a criterion, on the maximum particle size, for efficient inhibition is proposed. Thereafter, a one-dimensional methane/air flame traveling in a premixed gas loaded with sodium bicarbonate is simulated using a chemical mechanism based on GRI-Mech, extended to include inhibition chemistry and reduced to 20 species with a DRGEP method (Pepiot-Desjardins and Pitsch, 2008). Inhibitor particle size and mass loading are varied to study the flame response to inhibition by (NaHCO3)s powders. Finally, two-dimensional simulations of a planar flame traveling in a flow with a non-uniform inhibitor mass loading distribution are analyzed. In the case of strong particle stratification, an acceleration of the flame is observed, instead of a mitigation. This fundamental mechanism may limit the actual potential of inhibition powders in real configurations.