Dynamic simulations are performed for the NASA planned propulsive small expendable deployer system (ProSEDS) space tether mission using two finite element analysis codes. The first is a specialized code for simulating tethered space systems. The second is an in-house flexible multibody dynamics code adapted herein for modeling tethered satellites. The simulation of the ProSEDS mission is divided into two operations: a tether deployment operation and an electrodynamic operation. The specialized code uses a fixed number of nodes and finite elements in simulating the deployment operation, while the in-house code uses a variable number of nodes and elements. The application of each approach is discussed. A fuzzy-set technique is used in conjunction with the two codes to assess the effect of parameter variations on the deployment and electrodynamic operation of the ProSEDS tether. Detailed numerical simulations reveal that the deployment operation is not sensitive to variations in material parameters, but is sensitive to variations in the initial tether ejection momentum and to controller parameters. The electrodynamic operation is found to be highly sensitive to variations in earth's magnetic field and, to a lesser extent, variations in material and plasma parameters.