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In this paper the massive neutrinos model arising due to the Snyder noncommutative geometry, proposed recently by the author is partially developed. By straightforward calculation it is shown that the masses of the chiral left-and right-handed Weyl fields treated as parameters fixed by experiments, lead to the consistent physical picture of the noncommutative geometry, and consequently yield upper and lower energy limitations of a relativistic particle and exact integrability within the proposed model. This feature of the model in itself both defines and emphasizes its significance and possible usefulness for both theory as well as phenomenology for high energy physics and astrophysics. Basing on the model we discuss also the spacial case within the model describing ultra-relativistic neutrinos. Keywords: models of neutrino mass ; noncommutative geometry models ; Snyder noncommutative geometry ; energy renormalization ; exactly integrable systems ; Planck scale effects ; ultra-relativistic neutrinos ; Weyl equation ; Dirac equation, Introduction It was established recently by the author that the Dirac equation modified by the [gamma].sup.5]-term arising due to the Snyder noncommutative geometry model, yields the conventional Dirac theory with [...]