Hydraulic crawler excavators have been widely used for construction in industry, mining, and agriculture because of their special ability to work on weak soil support. However, the elastic properties of the ground increase the undesired vibrations of the entire operating machine. These oscillations significantly influence the working productivity, the level of fuel expenditure, and the comfort of the driver. There have been many works addressing this problem, although they mainly focus on mechanical dampers. Considering the system from robotic and control aspects, this study presents a new approach to deal with the abovementioned problem. A controller design, which uses a combination of feedback linearization and sliding mode control, is proposed based on a dynamic model. This control law reduces the vibrations of the system working on an elastic foundation, while also allowing for accurate tracking performance of the links. This control law is applied to a small-scale platform to investigate its feasibility for practical applications.