The article examines how discourse participants use language, the body and the local interactional and material context in the construction of offers. The data consist of eight hours of video recordings of everyday interactions in English and Finnish, and conversation analysis is used as the method. We focus on offers that make available to the recipient some concrete referent or material object or artifact in the current situation, that is, ‘concrete offers’. The article shows that such offers can be conceptualized (...) as consisting of two interlinked actions, one identifying the referent and the other explicating the offer. The article further argues that the frequent accomplishment over time of such complex actions may contribute to the emergence of a set of social action formats for offers. This action combination is explored by discussing offers that range from fully linguistically articulated ones, to types where embodied actions take an increasingly central role. (shrink)