Linear landscape elements, such as field margins, are agricultural practices whose adoption is supported by agri-environmental climate measures (AECMs). AECMs are meant to improve ecological conditions on farms and surrounding areas. The effectiveness of AECMs to enhance the supply of multiple ecosystem services (ESs) is still debated and knowledge on the resulting ESs bundles under different practices stemming from AECMs is still lacking. We aimed at assessing the potential of AECMs that promote the implementation of linear landscape elements to provide high levels of multiple ESs and at analyzing bundles at landscape level in different geographical contexts. We assessed the potential effects of linear landscape elements (woody, grassy, flower and a mix) on six ESs (food and feed provision, pollination, pest control, climate regulation, aesthetics, and habitat maintenance), combining scenarios and spatially explicit modelling approaches. Our results showed the positive effects of linear landscape elements on all regulating and cultural ESs. The more abundant the linear elements, the higher the overall ESs supply. However, the effect of linear landscape elements on multiple ESs depended on the types of linear elements and the geographical context of their implementation. When the supply of the ES was already high in the baseline situation, the changes induced by the implementation of the linear elements were much lower than when the baseline situation showed a lower initial supply of one or several of the ESs. Our analyses give insights on the efficiency of AECMs on multiple environmental targets. Our approach is a first step towards a general framework for an ex-ante integrated analysis of AECMs that can be used to design agri-environmental policies. From a more practical perspective, our results can form a basis for additional payments for AECMs. Our study also confirms the relevance of the EU biodiversity strategy that commits to ensure at least 10% of agricultural area as high-biodiversity landscape features such as linear landscape elements, and the relevance of the enhanced conditionality and eco-schemes in the reformed Common agricultural Policy targeting non-productive elements and biodiversity.