A kangaroo-like hopping machine with a mass-less springy leg, a body with centre of mass offset from the line of action of the spring find a tail link has been investigated in this study. Equations of motion in stance and flight phases are presented in this article. The equations determining the jump in velocities at the instant of touchdown are also formulated, based on impulse equations. The model has been used to simulate hopping motion for some select sets of parameters and initial conditions. Such a model can be used to develop largely passive, underactuated hopping systems, where relatively small actuators may suffice to compensate for the energy losses and to correct any deviations from a largely passive hopping trajectory.