A numerical solution, using the general formulation of the transcendental equation and eigenmode values, is proposed to demonstrate number of strongly guided modes propagating in sapphire crystal fibers (SCF). The SCF is considered to have hexagonal geometry of a single crystal and multimode step-index profile. Several distinguished characteristics are naturally embedded in SCF compared to other ordinary optical fibers. The eigenmodes of the SCF are numerically determined and are a combination of transverse electric, transverse magnetic, and hybrid modes. The numerical solution for wave-guiding in ultra-violet (UV), visible infrared (VIS/IR) spectrum, is investigated by the number of modal propagations under strongly guided approximation. The cross-sectional energy distribution of fundamental mode (FM) and higher order modes (HoM) describe the variation of the effective mode index with respect to the change in the core radius. The proposed waveguide is of ~35micron radius, exhibit −0.077 dB/m confinement loss at 200 nm. The simulations in this study are performed by the COMSOL multi-physics® software.