The breakdown phenomena of materials is a very complex process which involves a study of formation of microscopic cracks, their evolution to the other regions of the materials via some interaction and the ultimate collapse of the structure [1]. Random Fibre Bundle Model (RFBM) [2, 3] is a paradigmatic model, simple yet subtle, which captures the essential physics of breakdown processes. It consists of N parallel, vertical fibres whose ends are connected to two horizontal rods. The upper rod is fixed and a load F is applied to the lower one so that a stress σ (= F/N) is generated on each fibre. The fibres are assigned a threshold strength chosen randomly from a cumulative distribution function P (σ) with a corresponding density function ρ (σ). © 2006 Springer.