Based on the Hamilton theory and transforming the formulation into a discrete style, the model of a rotational flexible beam was established. Based on this model and the principle of the central difference method, we presented a subcycling algorithm for the flexible beam dynamics and established the commonupdate format and the substep update format. During the subcycling procedure, the computational precision and stability were assured by means of changing the step sizes. Computational results illustrate that the subcycling can enhance the computational efficiency significantly with suitable integral accuracy, and the computational stability can be enhanced by means of modifying the step sizes. As a result, the stiffness problem of the difference equation is solved effectively.