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An edge crack in a strip of a functionally graded material (FGM) is studied under transient thermal loading conditions. The FGM is assumed having constant Young's modulus and Poisson's ratio, but the thermal properties of the material vary along the thickness direction of the strip. Thus the material is elastically homogeneous but thermally nonhomogeneous. This kind of FGMs include some ceramic/ceramic FGMs such as TiC/SiC, MoSi2/Al2O3 and MoSi2/SiC, and also some ceramic/metal FGMs such as zirconia/nickel and zirconia/steel. A multi-layered material model is used to solve the temperature field. By using the Laplace transform and an asymptotic analysis, an analytical first order temperature solution for short times is obtained. Thermal stress intensity factors (TSIFs) are calculated for a TiC/SiC FGM with various volume fraction profiles of the constituent materials. It is found that the TSIF could be reduced if the thermally shocked cracked edge of the FGM strip is pure TiC, whereas the TSIF is increased if the thermally shocked edge is pure SiC.