The cosmological origin of $gamma$-ray bursts (GRBs) is now commonly accepted and, according to several models for the central engine, GRB sources should also emit at the same time gravitational waves bursts (GWBs). We have performed two correlation searches between the data of the resonant gravitational wave detector AURIGA and GRB arrival times collected in the BATSE 4B catalog. No correlation was found and an upper limit bbox{$h_{text{RMS}} leq 1.5 times 10^{-18}$} on the averaged amplitude of gravitational waves associated with $gamma$-ray bursts has been set for the first time.
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