Joining by compression of metallic inserts has been recently developed by the authors to create invisible lap joints between metal and polymer laminates. This paper revisits the process with the objective of proposing a new type of bi-material (polymer–metal) cylindrical insert for lightweight construction applications that is capable of ensuring complete filling of the joint at the end of stroke without increasing the forming force and the risk of sheet bending. The presentation is built upon a combined experimental and finite element research work focused on the modes of deformation, formability limits, forming forces, and resistance strength that lap joints produced with the new bi-material cylindrical inserts are able to withstand before failing. Results allowed designing a simple and easy to fabricate bi-material cylindrical insert that overcomes the main problems that have been pointed out to the metallic inserts earlier proposed by the authors.