How cells position their organelles is a fundamental biological question. During Drosophila embryonic muscle development, multiple nuclei transition from being clustered together to splitting into two smaller clusters to spreading along the myotube's length. Perturbations of microtubules and motor proteins disrupt this sequence of events. These perturbations do not allow intuiting which molecular forces govern the nuclear positioning; we therefore used computational screening to reverse-engineer and identify these forces. The screen reveals three models. Two suggest that the initial clustering is due to nuclear repulsion from the cell poles, while the third, most robust, model poses that this clustering is due to a short-ranged internuclear attraction. All three models suggest that the nuclear spreading is due to long-ranged internuclear repulsion. We test the robust model quantitatively by comparing it with data from perturbed muscle cells. We also test the model using agent-based simulations with elastic dynamic microtubules and molecular motors. The model predicts that, in longer mammalian myotubes with a large number of nuclei, the spreading stage would be preceded by segregation of the nuclei into a large number of clusters, proportional to the myotube length, with a small average number of nuclei per cluster.