In this study, we develop lower-dimensional interface elements to represent preexisting fractures in rock material, focusing on finite element analysis of coupled hydro-mechanical problems in discrete fractures–porous media systems. The method adopts local enrichment approximations for a discontinuous displacement and a fracture relative displacement function. Multiple and intersected fractures can be treated with the new scheme. Moreover, the method requires less mesh dependencies for accurate finite element approximations compared with the conventional interface element method. In particular, for coupled problems, the method allows for the use of a single mesh for both mechanical and other related processes such as flow and transport. For verification purposes, several numerical examples are examined in detail. Application to a coupled hydro-mechanical problem is demonstrated with fluid injection into a single fracture. The numerical examples prove that the proposed method produces results in strong agreement with reference solutions.