Chalcogenide glasses are furnished with several beneficial features such as high nonlinear coefficient, and their low bulk material losses as compared to silica in mid-infrared (IR) spectral regime makes them doubtlessly as one of the excellent candidates with highly tunable optical characteristics. They have wide transparency in IR domain and can be drawn into fine optical fibers; moreover, possessing potential applications in nonlinear optics realm. We investigated the elementary modal characteristics of solid-core air/chalcogenide hexagonal microstructured optical fibers (H-MOFs) such as mode-index, near-field and far-field intensity patterns, mode-field diameters (MFDs), dispersion and nonlinear characteristics with different geometrical configurations by implementing an alternative theoretical model. Chalcogenide glass H-MOFs as a potential candidate for slow-light generation in IR regime is explored. Also, the utility of such fibers for evanescent field based sensing applications is examined. The strength of the model has been checked by comparing the results with experimental and those which are based on numerical simulation, as available in the literature. Relative errors are also quoted.