A cutting insert having a substantially polygonal upper surface, a lower surface, a side face with a flank, and a cutting edge formed at the intersection of the upper surface and the side face.The cutting edge has a first cutting edge, a second cutting edge, and a third cutting edge located between the first and second cutting edge at the corner of the polygon. The flank has a first flank corresponding to the first cutting edge, and a second flank corresponding to the second cutting edge. The first flank has an upper flank connected with the first cutting edge, a middle flank located on the lower surface side of the upper flank, and a lower flank located on the lower surface side of the middle flank.Assuming the clearance angle of the upper flank is alpha, the clearance angle of the middleflank is belta, the clearance angle of the lower flank is gamma, and the clearance angle of the second flank is epsilon, the alpha, belta, gamma and epsilon satisfy the relation alpha<belta<gamma<epsilon. The cutting insert is attached to a cutting tool, and a cutting method employs the cutting tool.