Abstarct: In this research, thermoelastic damping in axially functionally graded microbeam resonators is investigated using modified strain gradient theory. First, by adopting Hamilton principle, the governing equation of free vibration of tapered microbeam made of axially functionally graded materials is derived baxsed on modified strain gradient theory. The dimensionless natural frequencies of cantilever and clamped-clamped microbeams are obtained by the semi-analytical methods, Rayleigh-Ritz and Galerkin, respectively. Since, the Rayleigh-Ritz test function does not satisfy all the boundary conditions, the governing differential equation and all boundary exxpressions are converted to an integral equation. According to integral equation, natural frequencies are determined using power expansion series and shifted Legendre polynomials series for cantilevered microbeam and series of common orthogonal function for clamped-clamped microbeam. The results of semi-analytical methods and solution of integral equation are compared to results of available literatures which in many cases a good overlap among them is observed. Hence, it can be concluded that the selection of semi-analytic test functions satisfy certain boundary conditions, therefore they can offer an acceptable answer. The thermoelastic damping in homogeneous microbeam is investigated baxsed on the modified strain gradient and generalized thermoelasticity theories. The both complex frequency and entropy generation approaches are employed to determine the results of the quality factor and the critical thickness of microbeam resonator are obtained that the attenuation of critical thickness is maximum. By comparing some results of the quality factor baxsed on both approaches, an excellent agreement is observed between them. The thermoelastic damping in the microbeam resonator made of axially functionally graded materials are studied with respect to the length scale parameters and the thermal relaxation time which are related to the modified strain gradient and Non-Fourier heat conduction theories, respectively.