This work is titled Modelling and Simulation of a Reversible Chemical Batch Reactor The results of the modelling and simulation of a reversible batch reactor is presented. The system of Ordinary Differential Equation arising from the modelling were simulated using the classical (4.4) Runge - Kutta method on a Matlab software. Reasonable values of the rate constants K1, K2, K3 and K4 were employed in the analysis. Aterations in the rate constant values ranging from 0.5 to 1.0 for k3 was employed to see its effect on other rate constants with initial concentration values of CA = 1.0. Results of the concentration profile shows that component A falls from 1.0 mol/dm-3 to 0.04mol/dm-3, component B from 0 to 0.53mol/dm-3 then drops, to 0.18mol/dm-3, and component C rises from 0.0 to a maximum value of 0.70mol/dm-3.