When an object is lifted vertically, the normal force increases and decreases in tandem with tangential (load) force to safely avoid slips. For horizontal object transport, horizontal forces at the contact surfaces can be decomposed into manipulation forces (producing acceleration/deceleration) and grasping forces. Although the grasping forces must satisfy equilibrium constraints, it is not clear what determines their modulation across time, nor the extent to which they result from active muscle contraction or mechanical interactions of the digits with the moving object. Grasping force was found to increase in an experimental condition where the center of mass was below the contact plane, compared to when it was in the contact plane. This increase may be aimed at stabilizing object orientation during translation. In another experimental condition, more complex moments were introduced by allowing the low center of mass to swing around a pivot point. Electromyographic (EMG) activity recorded from several intrinsic and extrinsic hand muscles failed to reveal active feedback regulation of contact force in this situation. Instead, in all experimental conditions, EMG data revealed a strategy of feed-forward stiffness modulation. Multiple regression analysis revealed that muscle activity at remote digits (e.g. the index and ring fingers) was highly correlated with the contact force measured at another digit (e.g. the thumb). The data suggest that to maintain grasp stability during horizontal translation, predictable as well as somewhat unpredictable inertial forces are compensated for by controlling the stiffness of the hand through co-contraction and modulation of hand muscle activity.