The bubbled slab, a type of reinforced concrete (RC) slab with plastic voids, is an innovative design that employs a biaxial distribution of voiding formers within the slab to reduce the slab’s self-weight while preserving a load-carrying capacity that is approximately comparable to that of solid slabs. This paper presents a new approach for figuring out the effective critical shear perimeter of voided slabs using the reduced-volume concept of concrete. This approach aims to reduce the coefficient of variation of the current design standards, namely the ACI 318-19 and Eurocode 2, for assessing the slabs’ resistance to punching shear. Our experimental program investigated the impact of voiding former patterns and the location of an opening near a column on the punching shear resistance of biaxial hollow slabs. The factors under consideration included the opening’s size, location, and distance from the loaded area, as well as the voiding formers’ placement concerning the critical shear boundaries. The results of experiments on 10 full-scale, 2000 × 2000 × 230 mm, reinforced concrete biaxial voided slabs with an opening are presented in this study. Two design expressions were used to estimate the biaxial hollow slabs’ shear strength. These expressions take into account the reduced volume of concrete and the distribution of voiding formers up to the section from the periphery of the column. The proposed approach to determine the effective punching shear perimeter has the lowest coefficient of variation among the methods suggested by these standards. This indicates the validity of our proposed expressions. The coefficient of variation of the proposed expressions does not exceed 0.057.