Computationally efficient formulas were developed for calculating the Coulomb component of the stress tensor in Ewald summations for three-dimensional systems with two-dimensional periodicity. The computational efficiency and accuracy of the formulas were compared with existing computational methods for water systems in the shapes of cubes, quadratic prisms, and slabs, all with two-dimensional periodicity. For these three systems, the formulas in our method significantly reduced the computational time required, and yielded sufficiently accurate evaluations of the Coulomb component of the stress tensor.