As the modern workplace is dominated by submaximal repetitive tasks, knowledge of the effect of task location is important to ensure workers are unexposed to potentially injurious demands imposed by repetitive work in awkward or sustained postures. The purpose of this investigation was to develop a three-dimensional spatial map of the muscle activity for the right upper extremity during laterally directed submaximal force exertions. Electromyographic (EMG) activity was recorded from fourteen muscles surrounding the shoulder complex as the participants exerted 40N of force in two directions (leftward, rightward) at 70 defined locations. Hand position in both push directions strongly influenced total and certain individual muscle demands as identified by repeated measures analysis of variance (P < .001). During rightward exertions individual muscle activation varied from 1 to 21% MVE and during leftward exertions it varied from 1 to 27% MVE with hand location. Continuous prediction equations for muscular demands based on three-dimensional spatial parameters were created with explained variance ranging from 25 to 73%. The study provides novel information for evaluating existing and proactive workplace designs, and may help identify preferred geometric placements of lateral exertions in occupational settings to lower muscular demands, potentially mitigating fatigue and associated musculoskeletal risks.