Since stress singularity was found at the interface end in current specimen of pullout test, interface shear strength (IFSS) obtained from the tests loses its rationality . But a useful conclusion  is that when the wedge angle of the matrix is less than a critical angle, the singularity of stress field at the interface end of the specimen in micro-debond test nearly disappears. Following this conclusion, a conic specimen shown in Fig. 1 is presented, in which the wedge angle of the specimen is designed to be less than a critical angle in order to prevent the singular stress field occurred at the interface end. The conic specimen is designed for pullout test to avoid disadvantages inherent in the micro-debond test . An axisymmetric model of fiber/matrix system with arbitrary wedge angles at the interface end is used for the determination of critical wedge angle. With the aid of asymptotic analysis and variable separation, eigenvalue, λ, could be determined by a characteristic determinant. For a given fiber-matrix system, a curve representing the relationship between the stress singularity index and wedge angle could be obtained by solving the characteristic determinant. We define the critical wedge angle, θcr, as the corresponding singularity index of – 0.005. The design of a conic pullout specimen is also discussed. FEM analysis is adopted to calculate the distribution of interfacial stresses near the interface end with different wedge angle. The results verify the rationality of the principle of the design of conic pullout specimen for IFSS measurement.