The elastic stress and strain fields of a finite-thickness plate containing two interacting holes are systematically investigated using the finite element method. The maximum stress and strain concentrations occur on the mid plane only in the thin plates. They do not occur on the mid plane and their locations are different in the same plate for the thick plates. The values of the maximum stress and the strain concentration factor and their locations depend on the distance between the two holes and the plate thickness. The stress and the strain concentration factor are different, even if in an elastic state. The stress concentration factor and the strain concentration factor on the plate surface decrease rapidly with increasing thickness and becomes lower than the values corresponding to the plane stress state and the values of the mid plane. They are too low to reflect the overall stress concentrations as the plate thickness increases. The differences between the maximum value and the surface value of the stress concentration factor, the strain concentration factor increase rapidly and tend to their respective constant values with increasing plate thickness. These constant values depend on the distance between the two holes and the difference of the stress concentration factor is larger than that of the strain concentration factor in the same plate.