AbstractA dynamic mathematical model has been developed which is suitable for thermally coupled distillation processes. An algorithm known as the equation‐decoupled method was used for simulation. EPISODE software and LU decomposition method were adopted to solve the ordinary differential and algebraic equations of the model, respectively. The initial conditions, viz. a solution for the steady state of the process in dynamics simulation were obtained by means of modified Naphtali‐Sandholm algorithm. Research on the dynamic behaviour of thermally coupled distillation processes was carried out on two examples. It was found, via the dynamic simulation, that a disturbance in the distribution of vapour coupled stream has a large effect on the composition of vapour side withdrawal and, similarly, for liquid coupled stream, on that of liquid side withdrawal when the fraction of side withdrawal is fixed, and a smaller effect when the quantity of side withdrawal is fixed.