A fractal pore model is presented. These fractal pores are the constituents of the pore network of amorphous catalyst particles. The model is constructed in a fundamental and modular way for maximum flexibility. Both the topology of the pore space and the fractal pore axis and surface morphology are accounted for. Attention is focused on the fractal geometrical modeling of the pores. Expressions for pore tortuosity and accessible pore surface area are derived. The finiteness of the fractal scaling intervals is accounted for. A surface effectiveness factor is introduced to describe the apparent catalyst area or activity of strong diffusion limited reactions. Formula are derived both for uniform and supported catalysts. Some practical implications for catalyst design purposes are discussed.