Context. The earliest phases of the evolution of a massive star are closely related to the developement of an H II region. Hypercompact H II regions are the most interesting in this respect because they are very young, and hence best suited to study the beginning of the expansion of the ionised gas inside the parental core. Aims. We have analysed the geometrical and physical structure of the hypercompact H II region G24.78+0.08 A1, making use of new continuum and hydrogen recombination line data (H41α, H63α, H66α, H68α) and data from the literature (H30α, H35α). Methods. We fit the continuum spectrum with a homogenous, isothermal shell of ionised gas at 10⁴ K and derive the size of the H II region and the Lyman continuum luminosity of the ionising star. We also fit the recombination line spectra emitted from the same shell with a model taking into account expansion at constant speed. Results. The best fits to the continuum and line spectra allow the derivation of the Lyman continuum luminosity of the ionising star, H II region size, geometrical thickness of the shell, and expansion velocity. Comparison between the 5 cm and 7 mm brightness temperature distributions demonstrates that a thin layer of ionised gas of a few 1000 K at the surface of the H II region is necessary to reproduce the morphology of the continuum emission at both wavelengths. Conclusions. We confirm that the G24 A1 hypercompact H II region consists of a thin shell ionised by an O9.5 star. The shell is expanding at a speed comparable to the sound speed in the ionised gas. The radius of the H II region exceeds the critical value needed to trap the ionised gas by the gravitational field of the star, consistent with the observed expansion.