In many industries, the number of firms evolves non-monotonically over time. A phase of rapid entry is followed by an industry shakeout: a large number of firms exit within a short period. We present a simple timing game of entry and exit with an exogenous technological process governing firm efficiency. We calibrate our model to data from the post World War II penicillin industry. The equilibrium dynamics of the calibrated model closely match the patterns observed in many industries. In particular, our model generates richer and more realistic dynamics than competitive models previously analyzed. The entry phase is characterized by preemption motives while the shakeout phase mimics a war of attrition. We show that dynamic strategic incentives accelerate early entry and trigger the shakeout by comparing a Markov Perfect Equilibrium to an Open-loop Equilibrium.