This study models ultraviolet (UV) light photo-initiated cross linking in corneal collagen. Two critical parameters, namely the safety depth (z*) and the cross linking time (T*), are analyzed via both numerical and analytical formulas. z* is shown to be a decreasing function of the molar extinction coefficient and the concentration (C₀) of the initiator. A higher light intensity and a smaller initiator concentration require a shorter cross linking time (T*) to achieve a given cross link depth. For C₀ = 0.25 and 0.5 mM, the safety depths were z* = 695 μm and 390 μm, respectively. The surface cross linking times for light intensities of 10 and 30 mW were 16 s and to 5.3 s, respectively. However, the volume (z > 0) cross linking time increased with the corneal depth z*. T* (at z = 250 μm) is 2.5 times of the surface value (at z* = 0). Analytical formulas for T* and z* are derived and compared with the numerically fit equation.