Monte Carlo simulations have been performed for two simple models of a titrating polyelectrolyte : (i) a rigid rod and (ii) a freely jointed chain. Both models have fixed bond lengths, and the polyelectrolyte charges interact through a screened Coulomb potential. Chains consisting of 80-1000 monomeric units have been studied at three salt concentrations : 0.001, 0.01, and 0.1 M. Conformational properties and the apparent dissociation constant are reported as functions of chain length, chain ionization, monomer-monomer bond length, and salt concentration. Mean field expressions are compared to the simulation results and are, in general, found to be excellent approximations for the rigid rod, but they are also able to provide semiquantitative descriptions of the apparent dissociation constant for the freely jointed chain. Comparisons with experimental data show that the conformational properties of the flexible model can reproduce features of the titration curves, although the use of a screened Coulomb potential overestimates the response to changes in salt concentration.