This paper provides new evidence on how offshoring shifts relative labor demand for tasks at the industry level. A novel theoretical mechanism, based on sorting of heterogeneous workers into occupations with task dependent offshoring cost, guides estimation. Cost shares of tasks are linked to offshoring in a panel estimation using German data for 1998-2007. It is shown that offshoring shifts home country relative labor demand towards more complex tasks with higher relocation cost. This demand shift holds when controlling for an industry's skill composition and is particularly strong for offshoring to non-OECD countries.