Abstract: In this paper the principle of construction of a fractal surface is introduced,interpolation functions for a fractal interpolated surface are discussed,the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved,the theorem of fractal dimension of fractalinterpolated surface is derived,and the case that practical data are used ic interpolate fractal surface is studied.

Key words: fractal geometry, higher dimension fractals, fractal interpolated surface.fractal dimension