Traumatic brain injury (TBI) occurs when local mechanical load exceeds certain tolerance levels for brain tissue. Extensive research has been done previously for brain matter experiencing compression at quasistatic loading; however, limited data is available to model TBI under dynamic impact conditions. In this research, an experimental setup was developed to perform unconfined compression tests and stress relaxation tests at strain rates ≤90/s. The brain tissue showed a stiffer response with increasing strain rates, showing that hyperelastic models are not adequate. Specifically, the compressive nominal stress at 30% strain was 8.83 ± 1.94, 12.8 ± 3.10 and 16.0 ± 1.41 kPa (mean ± SD) at strain rates of 30, 60 and 90/s, respectively. Relaxation tests were also conducted at 10%-50% strain with the average rise time of 10 ms, which can be used to derive time dependent parameters. Numerical simulations were performed using one-term Ogden model with initial shear modulus μ(o)=6.06±1.44, 9.44 ± 2.427 and 12.64 ± 1.227 kPa (mean ± SD) at strain rates of 30, 60 and 90/s, respectively. A separate set of bonded and lubricated tests were also performed under the same test conditions to estimate the friction coefficient μ, by adopting combined experimental-computational approach. The values of μ were 0.1 ± 0.03 and 0.15 ± 0.07 (mean ± SD) at 30 and 90/s strain rates, respectively, indicating that pure slip conditions cannot be achieved in unconfined compression tests even under fully lubricated test conditions. The material parameters obtained in this study will help to develop biofidelic human brain finite element models, which can subsequently be used to predict brain injuries under impact conditions.