We model the opportunities and incentives generated by international tax differences for international profit shifting by multinationals. The model considers not only profit shifting arising from international tax differences between affiliates and parent companies, but also from tax differences between affiliates in different host countries. Our model yields the prediction that a multinational's profit shifting in a country depends on a weighted average of international tax rate differences between all countries where the multinational is active. Using a unique dataset containing detailed firm-level information on the parent companies and subsidiaries of European multinationals and information about the international tax system, we test our model and empirically examine the extent of intra-European profit shifting by European multinationals. On average, we find a semi-elasticity of reported profits with respect to the top statutory tax rate of 1.3, while shifting costs are estimated to be 0.6% of the tax base. International profit shifting leads to a substantial redistribution of national corporate tax revenues. Many European nations appear to gain revenues from profit shifting by multinationals largely at the expense of Germany.