With an increasing focus on long-term consequences of concussive brain injuries, there is a new emphasis on developing tools that can accurately predict the mechanical response of the brain to impact loading. Although finite element models (FEM) estimate the brain response under dynamic loading, these models are not capable of delivering rapid (∼seconds) estimates of the brain's mechanical response. In this study, we develop a multibody spring-mass-damper model that estimates the regional motion of the brain to rotational accelerations delivered either about one anatomic axis or across three orthogonal axes simultaneously. In total, we estimated the deformation across 120 locations within a 50th percentile human brain. We found the multibody model (MBM) correlated, but did not precisely predict, the computed finite element response (average relative error: 18.4 ± 13.1%). We used machine learning (ML) to combine the prediction from the MBM and the loading kinematics (peak rotational acceleration, peak rotational velocity) and significantly reduced the discrepancy between the MBM and FEM (average relative error: 9.8 ± 7.7%). Using an independent sports injury testing set, we found the hybrid ML model also correlated well with predictions from a FEM (average relative error: 16.4 ± 10.2%). Finally, we used this hybrid MBM-ML approach to predict strains appearing in different locations throughout the brain, with average relative error estimates ranging from 8.6% to 25.2% for complex, multi-axial acceleration loading. Together, these results show a rapid and reasonably accurate method for predicting the mechanical response of the brain for single and multiplanar inputs, and provide a new tool for quickly assessing the consequences of impact loading throughout the brain.