Mechanical oscillations are important for many cellular processes, e.g. the beating of cilia and flagella or the sensation of sound by hair cells. These dynamic states originate from spontaneous oscillations of molecular motors. A particularly clear example of such oscillations has been observed in muscle fibers under non-physiological conditions. In that case, motor oscillations lead to contraction waves along the fiber. By a macroscopic analysis of muscle fiber dynamics we find that the spontaneous waves involve non-hydrodynamic modes. A simple microscopic model of sarcomere dynamics highlights mechanical aspects of the motor dynamics and fits with the experimental observations.