Meander coil is an important kind of coil configuration used in eddy current testing and electromagnetic acoustic testing. Owing to lack of analytical calculation formulas of impedance and magnetic field for meander coil, the analytical modeling is performed and a method of calculating pulsed response is presented. In terms of the general model for eddy current testing and electromagnetic acoustic testing, the calculation of impedance and pulsed magnetic field is transformed into the superposition of impedance and pulsed magnetic field of single rectangular coils. Based on the second order vector potential and the time harmonic magnetic field equations, the scalar potential analytical expressions of the meander coil are derived. Then the analytical expressions of magnetic flux in all solution area and eddy current in the specimen are obtained. By calculating the induction electric potential and the impedance change, the impedance analytical expression of the rectangular meander coil is derived. An FFT-IFFT method is used to calculate the time domain response to pulsed magnetic field. A model with an 8-meander double-layer double-bundle coil above an aluminium plate is used in calculation, and the results are in good agreement with the experimental result and the TSFEM calculation result, which verifies the analytical model and the accuracy of the calculation method. The analytical calculation largely shortens the calculation time compared with that by TSFEM method.