The paper presents an experimental and modeling study of the chemical structure of laminar premixed stoichiometric H2/CH4/C3H8/O2/Ar flames stabilized on a flat burner at 1, 3, and 5 atm. The flame structure was simulated using four different detailed chemical kinetic mechanisms proposed in the literature for oxidation of small hydrocarbons. The width of the zone of consumption of the fuel components was shown to differ appreciably at the three pressures. Hydrogen was shown to have the largest consumption zone, while propane has the smallest one. The kinetic analysis provided an explanation for the observed phenomenon, which assumes the formation of additional pathways for hydrogen and methane production in the flames of ternary fuel mixtures. Comparison of the measured and simulated flame structures shows that all the mechanisms satisfactorily predict the mole fraction profiles of the reactants, products, and some intermediates at atmospheric and elevated pressures. It is noteworthy that the mechanisms adequately predict the spatial variations in the mole fractions of free radicals, including the H, OH, and CH3, within the pressure range. However, some drawbacks of the mechanisms used have been identified. The mechanisms were shown to overpredict the mole fractions of some unsaturated hydrocarbons, including ethylene and acetylene, at elevated pressures. Therefore, the rate constants of the crucial reactions responsible for production/consumption of these species, as well as their pressure dependences, should be specified, and the mechanisms should be refined. To provide a deeper insight into the combustion chemistry of ternary fuel mixtures, one should focus on the structure of rich flames.