A cane tip has a body having an upper portion and a lower portion provided with a preferably concave traction surface. The lower portion tapers toward the upper portion and includes three preferably narrow, substantially planar regions sloping down toward the traction surface interposed by three preferably arcuate, web-like regions which together form a generally compact triangular footprint having truncated corners and arcuate sides. The body includes a bore which enters through the upper portion of the body and terminates above the traction surface and which receives and holds the lower end of the cane. The bore preferably includes a plurality of circumferential ribs which assist in securing the end of the cane. The traction surface preferably includes a circular central region and a plurality of structural branches radiating from the central region. A reinforcing plate is preferably provided in the body between the bore and the traction surface to prevent the end of the cane from inadvertently rupturing the traction surface. A sleeve is also preferably provided for use between the end of the cane and the bore in the body to accommodate cane ends of varying sizes. The cane tip permits a cane provided therein to be self-standing.