In this paper, we present a systematic methodology for constructing LFT representations for general mechanical systems derived via Lagrange’s equations. The LFT representation allows for any nonlinear matrix second-order mechanical system to be transformed into an interconnection of an LTI system with a diagonal “uncertainty” block. This uncertainty block is, in fact, state-dependent. Sufficient conditions that ensure well-posedness of the LFT interconnection are given. Using such LFT representations, the stability properties of the system can then be analyzed using Linear Matrix Inequalities (LMIs).