[en] Highlights: • A coaxial stacking disjoint model of HTR-10 is studied. • The mathematic geometrical relationships about the model are studied in detail. • This model can achieve accurate initial criticality value of HTR-10 reactor. - Abstract: HTR-10 is quite different than conventional reactors due to its geometry, spherical fuel elements and random distribution of fuel elements and graphite balls. It is desired to built realistic and accurate reactor model. In this paper, the detailed mathematic geometrical relationships of HTR-10 are studied on HTR-10′s coaxial stacking disjoint model. The geometrical model of the full reactor is obtained by using lattice and universe facilities provided by SuperMC. Compared with available data, this model can achieve accurate results in terms of initial criticality of the HTR-10 reactor.