Typical skeletal muscle experiment shows a region on a force-length curve where total tension decreases with length which suggests instability. In spite of this evidence, unstable behavior has not been demonstrated by direct observations. Although the controversial force-length relation has been discussed extensively in the past fifty years no quantitative theory explaining the mechanism of stabilization has been suggested. In this lecture we discuss a new mathematical model of a muscle fiber, suggesting that passive elasticity coming from the surrounding connective tissue may play a crucial role in its mechanical stability. The new theory possesses interesting mathematical structure with the curious appearances of measure valued solutions and devil staircases (joint work with I. Novak).