Computational simulation is a very powerful tool to analyze industrial processes to reduce operating risks and improve profits from equipment. The present work describes the development of some computational algorithms based on the numerical method to create a simulator for the continuous casting process, which is the most popular method to produce steel products for metallurgical industries. The kinematics of industrial processing was computationally reproduced using subroutines logically programmed. The cast steel by each strand was calculated using an iterative method nested in the main loop. The process was repeated at each time step (Δt) to calculate the casting time, simultaneously, the steel billets produced were counted and stored. The subroutines were used for creating a computational representation of a continuous casting plant (CCP) and displaying the simulation of the steel displacement through the CCP. These algorithms have been developed to create a simulator using the programming language C++. Algorithms for computer animation of the continuous casting process were created using a graphical user interface (GUI). Finally, the simulator functionality was shown and validated by comparing with the industrial information of the steel production of three casters.