Polyolefin fibre reinforced concrete (PFRC) has become an attractive alternative to steel for the reinforcement of concrete elements mainly due to its chemical stability and the residual strengths that can be reached with lower weights. The use of polyolefin fibres can meet the requirements in the standards, although the main constitutive relations are based on the experience with steel fibres. Therefore, the structural contributions of the fibres should be assessed by inverse analysis. In this study, the fibre dosage has been fixed at 6kg/m³ and both self-compacting concrete and conventional concrete have been used to compare the influence of the positioning of the fibres. An idealized homogeneous distribution of the fibres with such fibres crossing from side to side of the specimen has been added to self-compacting concrete. The experimental results of three-point bending tests on notched specimens have been reproduced by using the cohesive crack approach. Hence, the constitutive relations were found. The significance of this research relies on the verification of the formulations found to build the constitutive relations. Moreover, with these results it is possible to establish the higher threshold of the performance of PFRC and the difficulties of limiting the first unloading branch typical of fracture tests of PFRC.