The identification of the kinaesthetic information used for directing 3D multi-joint arm movements toward a target remains an open question. Several psychophysical studies have suggested that the ability to perceive and control the spatial orientation of our limbs depends on the exploitation of the eigenvectors (e (3)) of the inertia tensor (I ( ij )), which correspond to the arm rotational inertial axes. The present experiment aimed at investigating whether e (3) was used as a collective variable to direct the masses toward the target and hence to control the spatial accuracy of the final hand position. Natural, unconstrained, three-dimensional multi-joint reaching movements were submitted to alterations of forearm mass distribution. Given the existence of several "sensorimotor strategies" for the control of arm movements, the participants were a priori contrasted and ranged in groups according to their reliance on either visual or kinaesthetic information. The results indicated (1) the dependency of the arm's directional control on I ( ij ) parameters, (2) a non-linear relationship between the performance predicted by the inertia tensor and the observed performance, depending on the deviation amplitude and (3) the presence of a large inter-individual variability suggesting the existence of different strategies, including proprioceptive compensation mechanisms. This study validates in unconstrained multi-joint arm movements the exploitation of the inertia tensor by the central nervous system, thus simplifying the coordination of the segments' masses during reaching. The results also provide evidence for the existence of motor alternatives in exploiting proprioceptive information that may depend on spatial referencing modes.