Abstract: The effects of Kerr nonlinearity on Airy beams are investigated using the nonlinear Schrdinger equation. Based on the method of moments, the evolution of effective beam width is analytically obtained as well as the collapse power for Airy beams propagating in Kerr medium. Numerical simulations indicate that central parts of the major lobe of Airy beams give rise to initially radial compression during propagation even though the root-mean-square beam width broadens. Partial collapse of the central parts will appear for input power below the threshold for a global collapse. The field distributions of Airy beams are different during propagation in different media while the profiles and trajectories of the beams still remain invariant. In focused Kerr medium, the field of Airy beams is focused on center. In disfocused Kerr medium, it is dispersed.