Compression mouldings of commercial SMC were performed with an instrumented industrial press under various process conditions. Results underline the influence of process parameters such as the initial SMC temperature, the axial punch velocity and the geometry of the mould on local normal stress levels. They also show negligible fibre-bundle segregation in the principal plane of the moulded parts. Thereby, a one-phase plug flow shell model is proposed as a direct extension of the plug flow model proposed by M.R. Barone and D.A. Caulk [J Appl Mech 53(191):1986;361–70]. In the present approach, the SMC is considered as a power-law viscous medium exhibiting transverse isotropy. The shell model is implemented into a finite element code especially developed for the simulation of compression moulding of composite materials. Simulation and experimental results are compared, emphasizing the role of the SMC rheology on the overall recorded stress levels. Despite the simplicity of the model, rather good comparisons are obtained.