A new numerical approach to the solution of dynamic problems of countercurrent systems-the "Cinematic" model-has been developed. This model enables rapid computation of dynamics of such systems as described by systems of hyperbolic partial differential equations. In this paper the "Cinematic" model is illustrated with a gas absorption problem and a heat exchanger problem. It is found that the model is computationally simple and accurate in simulating the dynamic behaviour of the countercurrent heat and mass transfer processes considered. An important feature is that the "Cinematic" model does not demand any additional efforts in transforming the numerical results into the time domain. Laplace transforms or the method of characteristics always demand further transformations which prove to be computationally expensive when they lead to successful simulations. In addition to this, the model is found to be unaffected by the usual numerical problems of convergence and stability which are observed with finite-difference approaches.