The Cohesive Crack Model (CCM) is the most commonly accepted discrete crack approach for modelling concrete based materials. It is applied to Ultra High Performance Fibre Reinforced Concrete (UHPFRC) in this study because it can be easily represented as cohesive interface elements (CIE) in finite element modelling (FEM). CCM using a bilinear traction-separation relationship is used to simulate the load-deflection behaviour of UHPFRC test specimens. CCM based numerical simulation of three-point bend specimens are implemented using cohesive elements in ABAQUS FE software. Progressive crack propagation and failure mechanism of UHPFRC test specimens are simulated in order to predict their load capacities. Comparison of the simulation to existing experimental test results indicates that CCM with a bilinear traction-separation curve can provide predictions of both the loaddeflection curves and peak load of 100 and 150mm deep UHPFRC test specimens to =/- 6 % of the average for 50 and 100mm wide beams and to =/+20% for 150mm wide beams. Model predictions of the peak load for the 50mm wide and 50mm deep beams were to =/-25% of the average.