Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2332 2022 2022 University of Debrecen, Department of Mathematical and Computational Science, Debrecen, Hungary Warshine Barry The phenomenon of the failure of rotating mechanical structures is considered one of the dangerous phenomena that researchers are trying to study to find effective ways to avoid it. Many mathematical models describing the mechanism of crack formation in structures and the occurrence of failure in them have been adopted. In this paper, a computer simulation model of the failure mechanism in the intermediate conduction shaft of the ship's propeller (oil shuttle tanker) was designed based on the mathematical model that describes the stages of failure according to the number of revolutions that the shaft bears and the dimensions of fatigue cracks in it. In the beginning, a detailed mathematical model of the crack propagation mechanism was deduced as an initial stage, through which the differential equations that express the failure of the shaft were described. In the second stage, numerical simulations were implemented using the Euler and Rung-Kutta numerical methods used in solving ordinary differential equations. Also, for both methods using the Matlab language to reach the results and accurate graphs and analyze them. In this way it is possible to predict the number of cycles that the column will bear before the collapse, and this will reduce the occurrence of sudden collapses and save time, effort, and costs. 2023 2023 08 14 10.54216/GJMSA.090201 https://www.americaspg.com/articleinfo/33/show/2332