This paper presents a rigorous analysis of quasistatic magnetic field penetration into multiple slits in a conducting plane loaded with a ferrite sheet. The Fourier transform is used to represent the magnetic vector potentials in the spectral domain and the mode matching technique is enforced to obtain a solution in rapidly converging series form, leading to numerically efficient results. Shielding effectiveness is investigated in terms of the geometrical parameters of multiple slits and ferrite sheet. The proposed method has been validated in comparison to finite-element method solution with good agreement.