This study describes the performed physics analyses to define and characterize the cold neutron source of the KIPT neutron source facility. The cold neutron source is designed to optimize the cold neutron brightness to the experimental instruments outside the radial heavy concrete shield of the facility. Liquid hydrogen or solid methane with 20 K temperature is used as a cold moderator. Monte Carlo computer code MCNPX, with ENDF/B-VI nuclear data libraries, is utilized to calculate the cold neutron source performance and estimate the nuclear heat load to the cold moderator. The surface source generation capability of MCNPX code has been used to provide the possibility of analyzing different design configurations and perform design optimization analyses with reasonable computer resources. Several design configurations were analyzed and their performance were characterized and optimized.