The behaviour of rigid pipes during backfilling, under soil weight, and traffic live loads has received considerable attention from researchers in the past. A significant number of numerical, laboratory, and full scale studies on the response of rigid pipes under these effects have been published, which provide clear guidelines for the likely behaviour of the pipe. However, these studies were conducted assuming full support for the pipe in the haunch zone, although proper haunch support is, in fact, difficult to achieve in practice. This study therefore focuses on the performance of shallow buried concrete pipes under traffic live loading with poor haunch support using three-dimensional finite element modelling. The three-dimensional finite element model has been developed and validated with available results from the literature. The Duncan-Chang hyperbolic soil model has been used to represent the soil material and the pipe behaviour is simulated with a linear elastic model. The live load considered in the analyses is based on the British Standard design requirement (two axles with a maximum axle load of 450 kN). The effect of the length of the unsupported haunch is considered in this study, with the low haunch support being modelled as a void with different lengths. The results show that the effect of poor haunch support causes significant increases in the stresses within the pipe and has implications for the design of rigid pipes.