Abstract: Mechanics based on a fractal dimension space is defined as fractal mechanics,According to fractal theory, fractal mechanics should be described hy introducing new space concepts and new mathematical tools,In this paper,space, measure and dimension are first introduced,Fractal space, Besov space and the method of fractal interpolation function are then described in details. Moreover,the definition of mechanical quantities and laws on a fractal boundary and a fractal body is discussed.