. "High accretion rate during class 0 phase due to external trigger" . . . . . . . . . . . . . . . . "Abstract. Recent observations indicate that some class 0 sources have accretion rates orders of magnitude higher than those of class I. We investigated the conditions for the high accretion rates of some class 0 sources by numerical calculations, modelling an external trigger. For no external trigger, we find that the maximum value of the accretion rate is determined by the ratio \u03B1 of the gravitational energy to the thermal one within a flat inner region of the cloud core. The accretion rate reaches \u223C10\u22124 M\u2299 yr\u22121 if the cloud core has \u03B1\u2273 2. For an external trigger, we find that the maximum value of the accretion rate is proportional to the momentum given to the cloud core. The accretion rate reaches \u227310\u22124 M\u2299 yr\u22121 with a momentum of \u223C0.1 M\u2299 km s\u22121 when the initial central density of the cloud core is \u223C10\u221218 g cm\u22123. A comparison between recent observational results for pre-stellar cores and our model with no triggered collapse indicates that the flat inner regions of typical pre-stellar cores are not large enough to cause accretion rates of \u223C10\u22124 M\u2299 yr\u22121. Our results show that the triggered collapse of the cloud core is more preferable for the origin of the high accretion rates of class 0 sources than no triggered collapse." .