This article develops a theory of multiunit auctions where short squeezes can occur in the secondary market. Both uniform and discriminatory auctions are studied and bidders can submit multiple bids. We show that bidders with short and long preauction positions have different valuations in an otherwise common value setting. Discriminatory auctions lead to more short squeezing and higher revenue than uniform auctions, ceteris paribus. Asymptotically, as the auction size approaches infinity, the two formats lead to equivalent outcomes. Shorts employ more aggressive equilibrium bidding strategies. Most longs strategically choose to be passive. Free riding on a squeeze by small, long players has no impact on these results, but affects revenue in discriminatory auctions.