The generating process of self-accelerating Airy beams is researched from the viewpoint of geometric optics, and the relationship between the phase distribution on the incident plane and the self-accelerating trajectory of Airy beams is analyzed based on the concept of tangent clusters. A iterated algorithm for calculating the phase distribution of the airy beam incidence surface based on the self-acceleration trajectory distribution function is proposed, and the formation principle of the self-healing property of Airy beams is also discussed. Two-dimensional Airy beams are generated by collimated laser modulated with spatial light modulator, and the features of these beams such as non-diffraction, self-healing and self-accelerating are verified. In addition, the one-dimensional Airy beams are modulated to generate autofocusing beams and Bessel-like beams.