Abstract: The Poisson silvers in polar and cylindrical coordinate systems are developed using Fourier-Chebyshev collocation spectral method based on matrix-matrix multiplication. Usually the singularities will appear in the solution to Poisson equation in polar and cylindrical coordinate systems by spectral method. To avoid such a problem, two methods are proposed to solve the Poisson equation. The first is introducing the Gauss-Radau collocation points, thus excluding the singularity at the origin. The second method is transforming the computing interval [0, 1] in radial direction into [-1, 1] and then introducing the Gauss-Lobatto collocation points, so as to exclude the singularity at the origin when the number of nodes is odd. And no extra pole conditions are required by both methods to avoid the singularity at the origin. The two methods are compared with each other and verified via 2D and 3D instances separately, and the results indicate that they arc direct, fast, and highly accurate.