In the last decades supply chains emerged that stretch across many countries. This has been explained with decreasing trade and communication costs. We extend the literature by analyzing if and how unilateral environmental regulation induces offshoring to unregulated jurisdictions. We first apply an analytical partial-equilibrium model of a two-stage production process that can be distributed between two countries and investigate unilateral emission pricing and its supplementation with border carbon taxes. To get a more comprehensive picture, we subsequently apply a computable general equilibrium model that includes a better representation of international supply chains. We find heterogeneous, but mostly positive effects of a unilateral carbon emission reduction by the European Union on the degree of vertical specialisation of European industries and explain these differences by heterogeneity in the emission-intensity and pre-policy vertical specialisation of sectors. Border taxes are successful in protecting upstream industries, but with negative side effects for downstream industries.