In this study, the general theory of fractality is discussed to provide a fundamental understanding of fractal geometry applied to heterogeneous material surfaces like pavement surface and rock surface. It is well known that many physical phenomena and systems are chaotic, random and that the features of roughness are found at a wide spectrum of length scales from the length of the sample to the atomic scales. Studying the mechanics of these physical phenomena, it is absolutely necessary to characterize such multi scaled rough surfaces and to know the structural property of such surfaces at all length scales relevant to the phenomenon. This study emphasizes the role of fractal geometry to characterize the roughness of various surfaces. Pavement roughness and rock surface roughness were examined to correlate their roughness property to fractality.