An algorithm has been developed and implemented in a computer program that allows the estimation of PF coil voltages required to start-up an axisymmetric plasma in a tokamak in the presence of eddy currents in toroidally continuous conducting structures. The algorithm makes use of an eigenexpansion technique to solve the lumped parameter circuit loop voltage equations associated with the PF coils and passive (conducting) structures. An example of start-up for CIT (Compact Ignition Tokamak) is included.