A simple model is presented to describe the elastic deformation of a spherical particle, by which a numerical approach is proposed to describe the quasi-stationary motion of an elastic particle translating in the laminar flow of a squared micro-channel based on the ‘Motion Relativity’. The behavior of the inertial lift exerted on an elastic particle is numerically investigated and the emphasis of this study is to reveal the influence on the inertial lift by the deformation of the elastic particle. Results indicate that there is always a transverse focused position for an elastic particle translating in a laminar micro-channel flow with low Reynolds number. The focused position of an elastic particle may shift closer to the centerline of the channel than that of a rigid particle, with the increased deformation of the elastic particle. The behavior of the inertial lift exerted on an elastic particle is similar with that exerted on a rigid particle but there is an extra lift exerted on an elastic particle, resulted by the deformation. This extra lift is always towards to the centerline of the channel and its magnitude may increase with the increased deformation of the elastic particle. The inertial lift can be divided into a “viscous component” and a “pressure component” while the latter is a critical formation mechanism for the inertial focus of elastic particles.