We present a LIGO search for short-duration gravitational waves (GWs) associated with soft gamma ray repeater (SGR) bursts. This is the first search sensitive to neutron star f modes, usually considered the most efficient GW emitting modes. We find no evidence of GWs associated with any SGR burst in a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190 lesser events from SGR 1806-20 and SGR 1900+14. The unprecedented sensitivity of the detectors allows us to set the most stringent limits on transient GW amplitudes published to date. We find upper limit estimates on the model-dependent isotropic GW emission energies (at a nominal distance of 10 kpc) between 3x10;{45} and 9x10;{52} erg depending on waveform type, detector antenna factors and noise characteristics at the time of the burst. These upper limits are within the theoretically predicted range of some SGR models.