International audienceCosmic string cusps produce powerful bursts of gravitational waves (GWs). These bursts provide the most promising observational signature of cosmic strings. In this letter we report stringent limits on cosmic string models obtained from the analysis of 625 days of observation with the LIGO and Virgo GW detectors. A significant fraction of the cosmic string parameter space is ruled out. This result complements and improves existing limits from searches for a stochastic background of GWs using cosmic microwave background and pulsar timing data. In particular, if the size of loops is given by gravitational back-reaction, we place upper limits on the string tension $G\mu$ below $10^{-8}$ in some regions of the cosmic strin...