The study aims to address the lack of design techniques for welded rectangular hollow sections connections made with offset, i.e., where the members of the branch adjacent to the connection are laterally shifted away from the chord centreline towards the chord web. To estimate the plastic resistance of the laterally offset truss-type RHS T-connection, a theoretical investigation was conducted. As a result, an analytical model has been developed and verified against the outcomes of a series of non-linear numerical simulations. During the construction of the model, specific attention was paid to the most general case of the branch location relative to the chord web, namely, the scheme of connection where adjacent vertical faces of the branch and chord members are in different planes is considered as prevailing. The proposed analytical model is an extension of a plastic mechanism model for traditional stepped rectangular hollow sections (RHS) T-connections. The model predicts the yield load and the post-yield response of the connections under concentrated load. The model presented in this paper is compared with other recently proposed methods of analytically determining limit loads of offset connections, and it provides reliable results in yield load computation. Moreover, the model yields sufficient accuracy in predicting the ultimate load for the offset connections with matched faces of the chord web and brace lateral surface.