The linearity of stimulated Brillouin scattering (SBS) is studied in detail for the first time. A closed-form expression which measures the linearity of an SBS system is derived. This expression allows one to design the region of linear operation, and the amount of Brillouin gain of an SBS system, by altering some basic system parameters. The theory presented is experimentally verified using an SBS-based microwave photonic filter structure. The effect of the length of the Brillouin medium on the linearity of the filter is investigated, and a 9.7 dB extension in the dynamic range is demonstrated by reducing the length of the fibre used as the Brillouin medium, from 25 to 0.57 km, while the filter stopband rejection level remains 30 dB.