It is generally believed that cosmological Gamma Ray Bursts (GRBs) are produced by the deceleration of relativistic objects with Lorentz factor (Gamma) >~ 100. We study the possibility that some GRBs are produced along with relativistic matter ejection from supernovae. In this model, it is quite likely that the matter has to travel through the progenitors thick envelope before generating GRBs. Under the assumption that the ejected matter is described as a single collective matter, we obtain constraints on the matter to have Gamma >~ 100 at the breakout of the progenitor. One advantage of considering this type of model is that the expected GRB energy is sufficiently large, in contrast to the GRB generation model by the shock breakout in the energetic supernova explosion. We find that in general the cross section of the matter has to be very small compared with the progenitors radius and thus the matter has to be bullet (or jet)-like rather than shell-like.
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