Recent observations of gamma‐ray bursts (e.g., x‐ray precursor, x‐ray tail, and cyclotron lines observed by Ginga) strongly suggest that the gamma‐ray burst source is associated with a magnetized neutron star. As an energy source model the shell flash is one of the most studied and its detonative wave has been suggested as an energy conversion mechanism from thermal energy to gamma‐ray photons. Here we present results of numerical simulations of shell flashes of a mass‐accreting neutron star. Models with mass accretion ratedM/dt≳10−13M⊙/yr do not trigger a detonative wave. A model withdM/dt≳10−15M⊙/yr is marginal and its recurrence time is ∼106yr, so that the detonative wave model is statistically inconsistent. An alternative mechanism of energy conversion would be an Alfve´n wave generated in a convective region of a deflagration wave. In this case, the Alfve´n wave is generated by a vibration of the magnetic field in the convective region where the thermal pressure is larger than the magnetic pressure. The amplitude of the Alfve´n wave is determined by the convective heat transport efficiency and its strength is weaker but its duration is longer than the case of a detonation shock wave.