We study the rheology of quick clay, an unstable soil responsible for many landslides. We show that above a critical stress the material starts flowing abruptly with a very large viscosity decrease caused by the flow. This leads to avalanche behavior that accounts for the instability of quick clay soils. Reproducing landslides on a small scale in the laboratory shows that an additional factor that determines the violence of the slides is the inhomogeneity of the flow. We propose a simple yield stress model capable of reproducing the laboratory landslide data, allowing us to relate landslides to the measured rheology.