Numerical analysis method was used to reduce the number of functionally graded material (FGM) layers for joining Si₃N₄-Al₂O₃ using polytypoid interlayer by estimating the position of crack. In the past, hot press sintering of multi-layered FGMs with 20 layers of thickness 500 μm each have been fabricated successfully. In this paper, thermal residual stresses were calculated using finite element method (FEM) to find the optimized number of layers and its thicknesses of FGM joint. The number of layers for FGM was reduced to 15 layers from 20 layers. Thicknesses were varied to minimize residual stresses within the layers while reducing the number of FGM layers. The damage caused by thermal residual stress was estimated using maximum principal stress theory and maximum tensile stress theory. The calculated maximum stress was found to be axial stress of 430 MPa around 90% 12H/10% Al₂O₃ area. For each case, calculated strength of each FGM layer by linear rule of mixture was compared with computed thermal residual stresses. Thermal analysis results correctly predicted the position of crack, and this position agreed well with fabricated joints. Therefore, this numerical analysis method can be applied to reduced FGM layers of crack free joint. Finally, new composition profile of crack free joint was proposed using FGM method.