The labor market is often asserted to be characterized by rigidities that make it difficult for older workers to carry out their desired trajectory from work to retirement. An important source of rigidity is restrictions on hours of work imposed by firms that use team production or face high fixed costs of employment. Such rigidities are difficult to measure directly. We develop a model of the labor market in which technological rigidity affects the age structure of a firm's work force in equilibrium. Firms using relatively flexible technology care only about total hours of labor input, but not hours of work per worker. Older workers with a desire for short or flexible hours of work are attracted to such firms. Firms using a more rigid technology involving team production impose a minimum hours constraint, and as a result tend to have a younger age structure. A testable hypothesis of the model is that the hazard of separation of older workers is lower in firms with an older age structure. We use matched worker-firm data to test this hypothesis, and find support for it. Specification tests and alternative proxies for labor market rigidity support our interpretation of the effect of firm age structure on the separation propensity. These results provide indirect but suggestive evidence of the importance of labor market rigidities.