Cusps of cosmic strings emit strong beams of high-frequency gravitational w
aves (GW). As a consequence of these beams, the stochastic ensemble of grav
itational waves generated by a cosmological network of oscillating loops is
strongly non-Gaussian, and includes occasional sharp bursts that stand abo
ve the rms GW background. These bursts might be detectable by the planned G
W detectors LIGO/VIRGO and LISA for string tensions as small as G mu simila
r to 10(-13). The GW bursts discussed here might be accompanied by gamma ra
y bursts.