We simulate the characteristics of the Galactic population of radio and gamma-ray pulsars using Monte Carlo techniques. At birth, neutron stars are spatially distributed with supernova-kick velocities in the Galactic disk and randomly dispersed in age over the past 109 years. From their birth location, the neutron stars are evolved in the Galactic gravitational potential to the present time. With a radio luminosity model, we estimate the radio flux and filter each pulsar through a selected set of radio-survey parameters determining a flux threshold. Using the features of recent polar cap acceleration models invoking space-charge-limited flow, a pulsar death region further attenuates the population of radio-loud pulsars, and gamma-ray luminosities are assigned. Assuming a featureless emission geometry of 1 steradian and with an alignment of the radio and gamma-ray beams, and for the case of no field decay and a death valley, our model predicts that EGRET should have seen 10 radio loud and 2 radio quiet, gamma-ray pulsars. GLAST, on the other hand, is expected to observe 93 radio-loud and 87 radio-quiet, gamma-ray pulsars of which 8 are expected to be identified as pulsed sources. .