Computer-optimized treatment plans, aimed to enhance tumour control and reduce normal tissue complication, generally require non-uniform beam intensities. One of the techniques for delivering intensity-modulated beams is the use of dynamic multileaf collimation, where the beam aperture moves and the field shape changes during irradiation. When intensity-modulated beams are delivered with dynamic collimation, the problem of intra-fraction organ motion can cause distortions to the desired beam intensities. Unlike static field treatments, where intra-fraction organ motion only affects the boundaries creating broad dose penumbra, the interplay of the movement of the beam aperture and the movement of the patient anatomy can create 'hot' and 'cold' spots throughout the field. The mechanism for creating these effects is not well understood. This paper provides a simple analytical model which illustrates the fundamental mechanism for creating the dosimetric variations in the target when both the beam aperture and the target move during irradiation. Numerical analysis was carried out which calculates the cumulative primary photon fluence, or beam intensity, received by each point in the target, for a given pattern of motion. The results show that, for clinically realistic parameters, the magnitude of intensity variations in the target can be greater than 100% of the desired beam intensity. The magnitude of the photon intensity variations is strongly dependent on the speed of the beam aperture relative to the speed of the target motion, and the width of the scanning beam relative to the amplitude of target motion. The effects of fractionation as well as methods of minimizing and eliminating the dosimetric effects of intra-fraction organ motion are discussed.