Three experiments investigated the grip force exerted by the fingers on an object displaced actively in the near-body space. In one condition (unimanual) the object was held by one hand with the tripod grip and was moved briskly back and forth along one of the three coordinate directions (up-down, left-right, near-far). In the second condition (bimanual) the same point-to-point movements were performed while holding the object with the index and middle fingers of both hands. In the third condition (bimanual) the object was held as in the second condition and moved along a circular path lying in one of the three coordinate planes (horizontal, frontal, sagittal). In all conditions participants were asked to exert a baseline level of grip force largely exceeding the safety margin against slippage. Both grip forces and hand displacements were measured with high accuracy. As reported in previous studies, in the two point-to-point conditions we observed an upsurge of the grip force at the onset and at the end the movements. However, the timing of the transient increases of the grip force relative to hand kinematics did not confirm the hypothesis set forth by several previous studies that grip modulation is a pre-planned action based on an internal model of the expected effects of the movement. In the third condition, the systematic modulation of the grip force also for circular movements was again at variance with the internal model hypothesis because it cannot be construed as a pre-planned action aiming at countering large changes in dynamic load. We argue that a parsimonious account of the covariations of load and grip forces can be offered by taking into account the visco-elastic properties of the neuromuscular system.