The electromagnetic radiation pressure is characterized by an oscillatory behavior when the targeted object is illuminated by an amplitude-modulated wave whose wave intensity changes over time. In this study, a theoretical formalism is developed to investigate the dynamic radiation pressure acting on a perfect electromagnetic conductor (PEMC) cylinder as a typical material exhibiting rotary polarization. The incident field is assumed to be a transverse magnetic (TM) plane wave driven at two slightly different frequencies. Using the modal expansion method in cylindrical coordinates as well as the short-term time average of the Maxwell’s stress tensor over the surface of the cylinder, the exact series expansions for the dimensionless dynamic radiation pressure function are obtained, which represents the radiation pressure acting on the cylinder per unit cross-sectional area and per unit wave energy density. Numerical computations are also performed with particular emphasis on the cross-term factor generated by the interference phenomenon of two primary waves at the beating frequency. The simulated results demonstrate that there is a slight decrease for the co-polarized component of the radiation pressure while a minor increase for the cross-polarized component with growing difference frequencies. Moreover, a significant modification caused by the mode conversion effect must be taken into account when the cylinder has an admittance close to one. Potential applications can be sought in non-contact particle manipulation using the dynamic oscillatory radiation pressure induced by amplitude-modulated electromagnetic waves.