For isometric tasks, shoulder muscle forces are assumed to scale linearly with the external arm load magnitude, i.e., muscle force ratios are constant. Inverse dynamic modeling generally predicts such linear scaling behavior, with a critical role for the arbitrary load sharing criteria, i.e., the "cost function". We tested the linearity of the relation between external load magnitude exerted on the humerus and shoulder muscle activation. Six isometric force levels ranging from 17 to 100% of maximal arm force were exerted in 24 directions in a plane perpendicular to the longitudinal axis of the humerus. The direction of maximum muscle activation, the experimentally observed so called Principal Action (PA), was determined for each force magnitude in 12 healthy subjects. This experiment was also simulated with the Delft Shoulder and Elbow Model (DSEM) using two cost functions: (1) minimizing muscle stress and (2) a compound, energy related cost function. PA, both experimental (PAexp) and simulated (PAsim), was expected not to change with arm forces magnitudes. PAexp of the mm. trapezius pars descendens, deltoideus pars medialis and teres major changed substantially as a function of external force magnitude, indicating external load dependency of shoulder muscle activation. In DSEM simulations, using the stress cost function, small non-linearities in the muscle force - external load dependency were observed, originating from gravitational forces working on clavicular and scapular bone masses. More pronounced non-linearities were introduced by using the compound energy related cost function, but no similarity was observed between PAexp and PAsim.