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With a variation in crack length, the stress intensity factors are obtained by a path independent contour integral in this work. The Chebyshev polynomials are employed using the finite block method for Functionally Graded Materials (FGMs) with two-dimensional fracture problems. By the mapping technique, a block of quadratic type is transformed from Cartesian coordinate to a normalised coordinate with 8 nodes. The new governing equations in terms of displacements are deduced in the mapping domain. All coefficients of Chebyshev polynomials are determined by considering governing equations, boundary conditions and connecting conditions for two blocks. The accuracy and convergence of the FBM with Chebyshev polynomials is demonstrated with four examples and comparison has been implemented with analytical solutions and different numerical approaches. [ABSTRACT FROM AUTHOR]