Present models for the representation of naturally fractured systems rely on the double-porosity Warren-Root model or on random arrays of fractures. However, field observation in outcrops has demonstrated the existence of multiple length scales in many naturally fractured media. The existing models fail to capture this important fractal property. In this paper, we use concepts from the theory of fragmentation and from fractal geometry for the numerical construction of networks of fractures that have fractal characteristics. The method is based mainly on the work of Barnsley  and allows for great flexibility in the development of patterns. Numerical techniques are developed for the simulation of unsteady single phase flow in such networks. It is found that the pressure transient response of finite fractals behaves according to the analytical predictions of Chang and Yortsos , provided that there exists a power law in the mass-radius relationship around the test well location. Otherwise, finite size effects become significant and interfere severely with the identification of the underlying fractal structure.