The cage model for polymer reptation is extended to simulate gel electrophoresis. With increasing electric field strength E, the drift velocity upsilon of a long polymer with length L shows three different regimes: (a) the linear regime where upsilon similar to E/L; (b) the quadratic regime where upsilon similar to E-2, independent of the length of the polymer; and (c) a regime where the velocity decreases exponentionally with E. The transition between regimes (a) and (b) occurs for field strengths E similar to L-1. The transition between regimes (b) and (c) occurs for some value E-h, for which L-1 much less than E-h much less than 1. The behavior in the first two regimes is in agreement with earlier reports on simulations of the Duke-Rubinstein model, and with experimental work on DNA polymers in agarose gel. The third regime is not reported for the Duke-Rubinstein model, probably because in this model, stored length cannot compile into hernias.