The validated finite element head model (FEHM) of a 3-year-old child, a 6-year-old child and a 50th percentile adult were used to investigate the effects of head dimension and material parameters of brain tissues on the head rotational responses based on experimental design. Results showed that the effects of head dimension and directions of rotation on the head rotational responses were not significant under the same rotational loading condition, and the same results appeared in the viscoelastic material parameters of brain tissues. However, the head rotational responses were most sensitive to the shear modulus (G) of brain tissues relative to decay constant (β) and bulk modulus (K). Therefore, the selection of material parameters of brain tissues is most important to the accuracy of simulation results, especially in the study of brain injury criterion under the rotational loading conditions.