Modern analyses of sea level changes due to glacial isostatic adjustment (GIA) are based on the classic sea level equation derived by Farrell & Clark (1976, Geophys. J.R. astr. Soc., 46, 647–667). The connection between global sea level variations and changes to ocean height that is assumed within this equation breaks down in the presence of a time-varying shoreline geometry. We present a generalized sea level equation that overcomes this difficulty. We also derive analytic expressions for, and present schematic illustrations of, the error in the ocean height change over finite time intervals introduced in published efforts to incorporate shoreline evolution into the theory of GIA-induced sea level change. This comparison includes studies of shoreline migration due to either local sea level changes or the growth and ablation of marine-based ice. We conclude that the theories applied by Johnston (1993, Geophys. J. Int., 114, 615–634), Milne (1998, PhD thesis, University of Toronto, Toronto) and co-workers are more accurate than the procedure advocated by Peltier (1994, Science, 265, 195–201; 1998a, Geophys. Res. Lett., 25, 3955–3958; 1998b, Rev. Geophys., 114, 615–634), although an improvement in the latter has recently been reported (Peltier & Drummond (2002, Geophys. Res. Lett., 29, 10.1029/2001GL014273). Our generalized theory is valid for any Earth model. In a companion paper we derive the equations necessary to treat the special case of a spherically symmetric, linear viscoelastic and rotating Earth, and we quantify errors associated with previous work.