Individual fiber amplifiers with increased average power while maintaining a narrow spectrum and excellent beam quality, enable power scaling of beam combined systems. To accomplish this, fiber amplifiers must contend with two well-known deleterious processes: thermal modal instability (TMI) and stimulated Brillouin scattering (SBS). Changing the fiber host material from silica glass to crystalline Yttrium Aluminum Garnet (YAG) has been reported as a potential means to increase the SBS and TMI power thresholds due to favorable material properties, mainly increased thermal conductivity and decreased electrostrictive constants. In this report, the development of numerical models to examine nonlinear effects in crystalline YAG fiber is described. Fiber simulation code previously developed at the Air Force Research Laboratory (AFRL) for silica are leveraged for crystalline gain media. Results show TMI threshold for a Ytterbium doped YAG (Yb:YAG) fiber 28 times higher than the equivalent silica fiber, and an increase in SBS threshold by over 250 times in YAG compared to silica. The investigations also include thresholds for Holmium doped YAG (Ho:YAG) and Thulium doped (Tm:YAG), which compare well with published experimental data.