The literature review about the shear linear properties of brain tissue reveals both a large discrepancy in the existing data and a crucial lack of information at high frequencies associated with traffic road and non‐penetrating ballistic impacts. The purpose of this study is to clarify and to complement the linear material characterisation of brain tissue. New data at small strains and high frequencies were obtained from oscillatory experiments. The tests were performed on thin porcine white matter samples (corona radiata) using an original custom‐designed oscillatory shear testing device. At 37°C, the results showed that the mean storage modulus (G′) and the mean loss modulus (G­″) increased with the frequency (0.1 to 6310 Hz) from 2.1±0.9 kPa to 16.8±2.0 kPa and from 0.4±0.2 kPa to 18.7±2.3 kPa respectively. The reliability of these new dynamic data was checked over a partially common frequency range by conducting similar experiments using a standard rheometer (Bohlin C‐VOR 150). Data were also compared in the time field. From these experiments, the relaxation modulus (G(t)) was found to decrease from 24.4±2.1 kPa to 1.0±0.3 kPa between 10^­­­−5 s and 270 s.