A turbo pump unit provides high pressure oxygen and fuel in a space shuttle main engine (SSME). This paper focused on rotordynamics, investigating its characteristics based on a numerical simulation of turbo pump finite element model. Speeds up to 50,000 rpm are considered, as well as the special problems related to elastic-ring, seal hydrodynamic force, shroud force and clearance-excitation farce. The rotordynamic prediction shows that the elastic-ring which is inserted between the casing and the outer race of ball bearing allows far an acceptable separate margin of first critical speed. Additionally, the results show that the floating ring seal, which have a peculiar ring, adds substantial stiffness and damping to the system as well as exhibits superior performance in terms of rotordynamic stability of system compared to the plain seal.