This article presents analytical solutions for a clamped-clamped adhesively bonded single lap joint with movement of supports and its application to studying the failure mechanism of carbon nanotube junctions in a tensile test. In the analytical model, the interface shear and normal stresses, movement of one support end, geometric nonlinearity, and the contact stresses between two cylinders are considered. Analytical solutions are derived for a clamped-clamped single lap joint with movement of one support end first, and then geometrically nonlinear finite element analysis is conducted to verify the present analytical solutions. An equivalent two-dimensional model is presented for a junction self-assembled by two carbon nanotubes, and the failure mechanism of the carbon nanotube junction is then studied by using the present analytical solutions. Structural performance of single lap joints with movement of support ends as boundary conditions is also investigated.