A hallmark of the human motor system is its ability to adapt motor patterns for different environmental conditions, such as when a skilled ice-hockey player accurately shoots a puck with or without protective equipment. Each object (stick, shoulder pad, elbow pad) imparts a distinct load upon the limb, and a key problem in motor neuroscience is to understand how the brain controls movement for different mechanical contexts. We addressed this issue by training non-human primates to make reaching movements with and without viscous loads applied to the shoulder and/or elbow joints, and then examined neural representations in primary motor cortex (MI) for each load condition. Even though the shoulder and elbow loads are mechanically independent, we found that some neurons responded to both of these single-joint loads. Furthermore, changes in activity of individual neurons during multi-joint loads could be predicted from their response to subordinate single-joint loads. These findings suggest that neural representations of different mechanical contexts in MI are organized in a highly structured manner that may provide a neural basis for how complex motor behaviour is learned from simpler motor tasks.