We present details of a modified phenomenological polar cap model of g
amma-ray emission from pulsars, introduced recently by Rudak and Dyks
(1998). The model attributes observed gamma-rays mostly to electron-po
sitron pairs created in magnetospheres by high energy curvature photon
s emitted by primary electrons. We show how the basic ingredient of th
e model - the number of created e(+/-) pairs - depends on the pulsar p
eriod, and the magnetic field, for two different prescriptions for the
energy of the primaries, and how it affects predictions for the gamma
-ray luminosity. The model has been successfully applied to the result
s of the Compton Gamma Ray Observatory (CGRO) observations.