  We analyze the electromagnetic production of K^+Lambda and K^0Lambda near
their production thresholds by using isobar models. In the K^+Lambda channel we
show that the model can nicely describe the available experimental data. In the
K^0Lambda channel we demonstrate that the K^0 charge form factor has sizable
effects on the longitudinal cross section. By extending the model up to W =
1730 MeV, we are able to observe the existence of the narrow P_{11} (J^p =
1/2^+) resonance in the kaon photoproduction process. It is found that the most
convincing mass (width) of this resonance is 1650 MeV (5 MeV).
