An appropriate algorithm of sequential modular flowsheeting is applied to steam cracking furnaces. The mathematical equations governing all parts of the furnace are explained and the programming procedure in simulation state is described. The application of the pseudo steady state approximation to solve the complex reaction network is reported as well. This lessens the convergence time drastically The results of the simulation are compared to industrial data. Finally using the verified model and via the proposed solution procedure, the required calculation steps and the corresponding time to solve the problem are improved. General considerations about the flowsheeting at transient states are also pointed out. For each time increment in transient state, a pseudo-steady flowsheet simulation has to be performed taking account of all transient contributions. Here the main complexity that may depress the convergence is the transient behavior of the radiant box (fire side), determining heat flux into the reactor (process side), as well as their mutual interactions. The tear streams in this process are inlet stream to the pyrolysis reactor, the fuel gas stream feeding into the burners, the temperature transmitter line for the high pressure steam produced, the gas stream entering the third bank, and also the flue gas entering the bank 5 of heat exchangers in convection section of the furnace. Overall, based on the proposed rigorous model for steam cracking furnaces and considering the nine-loop flowsheet which is handled by Westerberg tearing procedure, the flowsheeting problem for this important plant is organized and solved successfully. (C) 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.