Many industrial tasks require repetitive shoulder exertions to be performed with concurrent physical and mental demands. The highly mobile nature of the shoulder predisposes it to injury. The purpose of this study was to determine the effects of simultaneous gripping, at a specified magnitude, on muscle activity and maximal arm force in various directions. Ten female subjects performed maximal arm exertions at two different heights and five directions using both specified (30% maximum voluntary grip) and preferred (self-selected) grip forces. Electromyography was recorded from eight muscles of the right upper extremity. The preferred grip condition produced grip forces that were dependent on the combination of arm height and force direction and were significantly greater (arm force down), lower (to left, up and push forward), or similar to the specified grip condition. Regardless of the magnitude of the preferred grip force, specifying the grip resulted in decreased maximal arm strength (by 18-25%) and muscle activity (by 15-30%) in all conditions, indicating an interfering effect when the grip force was specified by visual target force-matching. Task constraints, such as specific gripping demands, may decrease peak force levels attainable and alter muscle activity. Depending on the nature of task, the amount of relative demand may differ, which should be considered when determining safety thresholds.