Process-induced thermal residual stresses and matrix failure of unidirectional carbon fibre reinforced composites (CFRP) have been investigated by finite element analysis (FEA). We used a partial discrete FEA model based on a unidirectional composite consisting of a microscopic area of fibres and matrix surrounded by a homogenised composite area. The FEA provided information about the stress state in the matrix and the fibre-matrix interface. The transverse strength of the composite was calculated regarding matrix failure and fibre matrix debonding. The influence of the temperature on the Young's modulus, the non-linear stress-strain behaviour and the strength of the matrix were investigated in detail. Following this approach it was possible to incorporate the resulting microresidual stresses on the transverse strength of the composite. Tensile tests of the neat resin and of the composite were performed in the temperature range of -40 degrees C to 60 degrees C. The results of the FEA modelling are in good agreement with the experimental results of the transverse tests.