This study considers the problem of robust interconnection and damping assignment passivity-based control approach (IDA-PBC) for underactuated mechanical systems from two points of view. First, the robustness of IDA-PBC in the presence of non-vanishing matched and unmatched uncertainties is analysed and sufficient conditions are derived to ensure ultimate boundedness of system. Second, the robust control design is provided by adding a new control input to the former controller designed by IDA-PBC, such that asymptotic stability of the closed-loop system in the face of non-vanishing matched uncertainties is fulfilled. Finally, the proposed robust controller is evaluated through simulations of two practical examples, i.e. an inertia wheel pendulum and a single-link elastic joint robot. The simulation outcomes clearly reveal the effectiveness of the presented robust controller.