This paper develops a theory of multiple unit auctions with short squeezes in the post- auction market. This is especially relevant for financial and commodity markets where players may enter the auction with established forward positions. We study how a potential short squeeze impacts on bidders’ strategies and auction performance. Conversely, we also study how the design of the auction affects the incidence of short squeezes. In particular, we model both uniform price and discriminatory price auctions in a true multiple unit setting, where bidders can submit multiple bids for multiple units. Our model is cast in what appears to be a common value framework. However, we show that the possibility of a short squeeze introduces different valuations of the to-be-auctioned asset between short and long bidders. Equilibrium bidding strategies depend on pre-auction allocations and the size of the auction. Short squeezes are more likely to happen after discriminatory auctions than after uniform auctions, ceteris paribus. Discriminatory auctions therefore lead to (1) more price distortion; (2) higher revenue for an auctioneer; (3) more volatility in the secondary market. This shows that a central bank or sovereign treasury, say, may face a tradeoff between revenue maximization and market distortions when choosing the design of repo or treasury auctions. The probability of a short squeeze following a discriminatory auction tends to decrease with the auction size, increase with the market power of the largest long bidders, and decrease with small long players’ scope for free-riding on a short squeeze. Asymptotically, as the auction size becomes arbitrarily large, the two types of auctions lead to equivalent outcomes.