We develop a model of an industry with many heterogeneous firms that face both financing constraints and irreversibility constraints. The financing constraint implies that firms cannot borrow unless the debt is secured by collateral; the irreversibility constraint that they can only sell their fixed capital by selling their business. We use this model to examine the cyclical behavior of aggregate fixed investment, variable capital investment, and output in the presence of persistent idiosyncratic and aggregate shocks. Our model yields three main results. First, the effect of the irreversibility constraint on fixed capital investment is reinforced by the financing constraint. Second, the effect of the financing constraint on variable capital investment is reinforced by the irreversibility constraint. Finally, the interaction between the two constraints is key for explaining why input inventories and material deliveries of US manufacturing firms are so volatile and procyclical, and also why they are highly asymmetrical over the business cycle.