Most striated muscles generate steady contractile tension when activated, but some preparations, notably cardiac myocytes and slow-twitch fibers, may show spontaneous oscillatory contractions (SPOC) at low levels of activation. We have provided what we believe is new evidence that SPOC is a property of the contractile system at low actin-myosin affinity, whether caused by a thin-filament regulatory system or by other means. We present a quantitative single-sarcomere model for isotonic SPOC in skeletal muscle with three basic ingredients: i), actin and myosin filaments initially in partial overlap, ii), stretch activation by length-dependent changes in the lattice spacing, and iii), viscoelastic passive tension. Modeling examples are given for slow-twitch and fast-twitch fibers, with periods of 10 s and 4 s respectively. Isotonic SPOC occurs in a narrow domain of parameter values, with small minimum and maximum values for actin-myosin affinity, a minimum amount of passive tension, and a maximum transient response rate that explains why SPOC is favored in slow-twitch fibers. The model also predicts the contractile, relaxed and SPOC phases as a function of phosphate and ADP levels. The single-sarcomere model can also be applied to a whole fiber under auxotonic and fixed-end conditions if the remaining sarcomeres are treated as a viscoelastic load. Here the model predicts an upper limit for the load stiffness that leads to SPOC; this limit lies above the equivalent loads expected from the rest of the fiber.