Material properties of brain tissue have been characterized under different modes of loading;​ however it has been shown that a constitutive model developed under one mode of loading (e.g. shear) may not necessarily predict the behavior of the tissue under another mode of loading (e.g. compression). In this study a viscoelastic constitutive model for brain tissue was developed that is capable of predicting the behavior of the tissue under multiaxial loading. Step and hold tests under shear and compression loading were performed on bovine brain samples with a strain rate of 10 s‐1 to strain levels of 30%. The applicability of quasilinear viscoelastic assumption was validated for strain levels up to 30% for shear and compression deformation. A generalized Rivlin model with 3 terms was considered and the response of this model to shear and compression was determined. These responses were used to determine the viscoelastic behavior under each mode of loading by fitting to the experimental model simultaneously. The hyperelastic material parameters and parameters of a relaxation function at 4 decay rates were determined. The developed model was compared with previously developed models and it showed a close agreement with them in their corresponding mode of loading, while having the advantage of modeling multiaxial loading as well.