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As a common tool for analyzing the response of pulsed eddy current, an analytical model has been widely paid attention because of its advantages, such as clear physical meaning, high accuracy, fast calculation speed, etc. In recent years, with the application of pulsed eddy current array probe, an analysis of the transmitter and receiver array unit (hereinafter referred to as TR probe), whose coils are not coaxial, is in urgent need. However, the component defect is always equivalent to a large area wall thinning defect in most of the analytical models of TR probe, which causes a low calculation accuracy. In order to improve the solution accuracy of the analytical model of the TR sensor, the component defect is equivalent to a flat-bottomed blind hole defect, an analytical model of the pulse eddy current TR probe for a component with a flat-bottomed blind hole is established, and a fast method to solve the analytical model is proposed: Firstly, by analyzing the typical model, it is found that the form of its analytical solution is composed of the product of generalized reflection coefficient, coil coefficient, etc. The generalized reflection coefficient is only related to the structure of the component, and the coil coefficient is only related to the probe. Then, by referring to the coaxial probe detection model with flat-bottomed blind hole component and the TR probe model with uniform wall thickness thinning defect, the analytical expressions of generalized reflection coefficient and coil coefficient are obtained, respectively. Finally, the analytical solutions of pulsed eddy current TR probe with flat-bottomed blind hole component can be calculated by combining these two coefficients. The correctness of the above analytical solution is verified by comparison with experimental data. The proposed method can be applied to the rapid solution of other pulsed eddy current analytical models, reducing the difficulty of solving analytical models.