A dynamic model of a novel oscillatory cutting brush for street sweeping in free rotation is developed. The bristles are modelled as cantilever beams. The equation of motion is determined through the theory of forced transverse vibrations of beams, and the solution is based on the normal-mode method. A sinusoidal angular speed function and a novel function, named VAP, are studied. The model is validated through finite element analyses. The effects of brush parameters on brush dynamics are identified. Notably, for the VAP function, a condition similar to resonance tends to occur in the stronger plane for bending deflections, when the frequency of the brush is an odd fraction of a natural frequency of the bristle for that plane. The model can also be applied to study the dynamics of a small-deflection cantilever beam, when the transverse external force is a squared, sinusoidal, triangle, or VAP wave.