The electromagnetic and weak neutral current matrix elements that ente
r in the analysis of parity-violating quasielastic electron scattering
are calculated using a continuum nuclear shell model, New approximati
ons to the on-shell relativistic one-body currents and relativistic ki
nematics for use in such models are developed and discussed in detail.
Results are presented for three closed-shell nuclei of interest: O-16
, Ca-40 and Pb-208. The current work concludes with a study of the sen
sitivity of the resulting parity-violating asymmetries to properties o
f the nucleon form factors including the possible strangeness content
of the nucleon.