The magnetic field,Hfj, of the first flux jump during the initial magnetization of synthetic high‐field superconductors, composed of indium in porous glass, has been measured as a function of the temperature and the field‐sweep ratedH/dt. The behavior is reasonably well described byHfj∝log(dH/dt). At low values ofdH/dt, logHfjis approximately proportional to 1/(dH/dt). It is shown that under rather special conditions the flux‐jumping behavior depends upon the condition of the sample surface.