Long-period variable stars (LPV's) are considered. Pulsations of the surface of such a star result in formation in the stellar atmosphere of a shock wave in each cycle of the star's variability, ionizing the circumstellar gas which, recombining, gives rise to emissions in optical lines hydrogen and metals. I show the recombining layer behind the shock front to be optically thick in the free-free continuum at the radio wavelengths as short as 1 cm. At the gas temperatures behind the front T = 20000 K, the radio flux density at 1 cm from the front surface at a distance of a few hundred parsees will be several or several tens of mjy. So far, the only positive result of searches for LPVS’ radio continuum is the detection of radio flux from R Aql, obtained at different epochs by several authors. In October 1978 R Aql showed radio emission of 5.3 mjy at 14.9 GHz (Bowers and Kundu, 1979), and in August 1985 - 0.54 mjy at the same frequency (Drake et al.. 1987); these figures are consistent with our model. Besides that, R Aql experienced stronger radio flares at longer wavelengths, up to a few hundred mjy (Woodsworth and Hughes, 1973; Estalella et al.. 1983); these cannot be explained by thermal radio emission and require a nonthermal mechanism (synchrotron or cyclotron maser).