A detailed numerical investigation has been carried out to investigate the effect of local fibre array irregularities on microscopic interfacial normal stress for transversely loaded unidirectional carbon fibre/epoxy composites with random fibre arrangement. Linear elastic finite element analyses were carried out for a two-dimensional image based model composed of 70 fibres. One fibre in this image based model is replaced with resin as the resin equivalent fibre, and the resulting change in microscopic interfacial normal stress distribution is investigated. Three fibres are selected for the resin equivalent fibres to clarify the individual local geometrical irregularity. Calculations were carried out for three loading conditions: case A, cooling of 2155 K from the curing temperature; case B, transverse loading of 75 MPa chosen as an example of macroscopic transverse fracture strength and case C, both cooling from the curing temperature and transverse loading of 75 MPa. The effect of fibre array irregularities on the interfacial stress state is limited to the region between the resin equivalent fibre and its first neighbouring fibres. The contribution of the second neighbouring fibre is small and that of further fibres is negligible.