The complex variable method was adopted to analyze the stresses and displacements around three-centered arch openings, and to investigate the mechanical behavior of such excavations in general. High stress concentrations occur at right-angle corners and small arch regions when subjected to far-field uniaxial compression. Increasing the lateral pressure factor (LPF) significantly magnifies the stress concentration factor (SCF) at right-angle corners and in large arch regions, and tangential compression is also evident. The growth rate of SCF is an invariant determined by the shape of openings, and it can not only determine the SCF for different LPF, but also characterizes opening boundary locations where the SCF is more sensitive to the LPF. In far-field uniaxial compression conditions, the roof of the opening is displaced downward, the floor is displaced upward, and the vertical walls expand. These deformational trends are gradually reversed with increasing LPF. As an example, these variations of stress and displacement are found in the transportation and mining roadways of the Beiminghe Iron Mine. In engineering practice, decreasing the height-to-span ratio in arched excavations increases their geometric curvature and increases the SCF.