Abstract: Thick conducting shielding plates exhibit strong skin effect under power-frequency and harmonic magnetic fields. Resolving the boundary layer near the conductor surface requires a fine mesh in the thickness direction. This enlarges the spectral radius of the diffusion operator and makes the semi-discrete system stiff. Explicit schemes are then limited by the stability step size, while implicit schemes become expensive under fine meshes because a large linear system must be solved at each step. For this problem, a structured precise integration method is developed for steady-state eddy-current loss evaluation in two-dimensional quasi-static thick conductors. The model is solved only in the conductor domain. The sinusoidal excitation on the upper surface is introduced through a Neumann boundary input, and the air region is not discretized explicitly. Time marching is carried out by a diffusion-type matrix-exponential update. The nonhomogeneous boundary input is treated by \phi -function convolution. For the Kronecker-separable discrete operator, the matrix-function action is implemented through Sylvester-type operator actions. Dense propagation matrices are therefore avoided, and the memory requirement is reduced. Numerical results show that the proposed method agrees with the reference results in cycle-averaged Joule loss. Under the same steady-state extraction, post-processing, and main-loop timing criteria, it gives a better error-versus-CPU-time relation than the Crank-Nicolson method and requires less memory under high-frequency fine-mesh conditions.