The results of the theoretical study of lasing in hollow cathode discharge (HCD) plasma are presented. The ion metal transitions were excited by second kind collisions at HCD of noble gas metal vapor mixtures, such as He-Be, Ar-Ca, Kr-Ca, Kr-Sr, Ne-Ga, Ne-In, He-In, Ne-Tl, and He-Tl. The dependences of the level population densities, gain and specific laser output power on HCD parameters are calculated. As a result, the lasing on 38 new transitions in the infrared wavelength range of 689…3724 nm were predicted. Studied lasers can become effective sourses of radiation for using in metrology