Using proven computational methods developed to efficiently treat transverse and longitudinal dynamic reshaping associated with single-stream propagation effects in cooperative light-matter interactions, a realistic superfluorescence (SF) theory was constructed in close collaboration with experimentalists. A semi-classical model based on the Maxwell-Bloch equa-tions (which rigorously encompasses diffraction, transverse density variations and inhomoge-neous broadening) is used. Furthermore, the medium initiation is stimulated by a coherent pulse of an area θ0 which varies radially, propagates along the rod axis and tips the indi-vidual Bloch vectors over an angle θ0 from its upright position. This effective initiation is treated in using either (a) an homogeneous average tipping angle or (b) instantaneous longitudinal and transverse fluctuations. The Cs datas are correctly simulated for the first time.* Important remark At this time, I wish to express my appreciation and give credit to Gibbs, McCall and Feld for their many contributions in the form of numerous relevant discussions, preparatory ana-lytical work and help in selecting details of realistic models based on their close contact with laboratory results. In addition, Dr Gibbs' participation in carrying the calculations accelerated the rate of progress in my research. Let me take this occasion to thank Dr. Gibbs, Dr. McCall and Dr. Feld for their energetic and enthousiastic collaboration.