A computationally efficient method was developed for calculating Coulomb interactions in three-dimensional (3D) systems with two-dimensional (2D) periodicity; the 2D particle-mesh Ewald (2D-PME) method we previously developed was extended. The formulation and numerical algorithms are described in detail for calculating the Coulomb potential energy, the Coulomb force, and the Coulomb component of the pressure tensor. Computational efficiency and accuracy of the 2D-PME method were evaluated for two water systems with 2D periodicity in the x and y directions and with non-periodicity in the z direction. Compared with exact results calculated by using the original 2D Ewald summations, the 2D-PME method yielded significantly accurate calculations, similar to the computationally efficient method we previously developed for calculating 2D Ewald summations (2D-EW method). For a given accuracy, the 2D-PME method was faster than the 2D-EW method for the water systems we examined. The computational effort of the 2D-PME method decreases as the computationally efficiency of the Fourier transforms used in the 2D-PME method increases. The 2D-PME method is therefore promising for accelerating molecular dynamics and Monte Carlo simulations for 3D systems with 2D periodicity.