Abstract: In recent years, fractal geometry has been adopted widely to make fracture analysis of materials. The deuelopment and main definitions of fractal geomelry, are introduced in short, in his paper, and fractal dimension estimations of simple irrigular curves are analysed. On the assumption that fracture surfaces can be classified as approxmately fractal, the fractal characterizations of fracture surfaces of materials are examined. The mechanics behaviours when the material fractured would be traced quantitatively by means of the fractal dimensions of fracture surfaces.