Actomyosin bundles such as muscle myofibrils, stress fibers and cytokinetic rings are used by cells to exert force, contribute to the cell's structural integrity and accomplish morphological change. In muscle and some types of stress fibers actin, myosin and other components are organized into sarcomeric repeat units but in many other cases the structure is far more disordered. The mechanisms whereby such disordered architectures produce tension are not established. Here we used mathematical modeling to quantitatively understand the behavior of reconstituted in vitro actomyosin bundles consisting solely of F-actin and myosin thick filaments. In the presence of ADP, actin and myosin formed stable (>1 hour), non-tensile bundles ∼5-50 microns long anchored between polystyrene beads. The myosin is initially uniformly distributed along the bundles. Upon addition of ATP, the bundles contracted and became taut while the myosin reorganized into discrete clusters. We developed a mathematical model to account for this behavior. The random actin filament locations and polarities leads to a random net actin polarity at different locations along the bundle. We found the self-organization of myosins into clusters is driven by the tendency of myosin to migrate to zeros of the polarity profile. In agreement with experiment myosin clusters develop over ∼10 s by myosin translation. We calculate the distribution of myosin cluster separations and predict the mean cluster separation increases with actin filament length. Thus, a minimal bundle of actin and myosin alone has the inherent capacity to self-organize into a heterogeneous structure exhibiting morphological similarity to tension-producing cellular actomyosin structures such as stress fibers.