The band structure of the dilute-As GaNAs material is explained by the hybridization of localized As-impurity states with the valance band structure of GaN. Our approach employs the use of Density Functional Theory (DFT) calculated band structures, along with experimental results, to determine the localized As-impurity energy level and coupling parameters in the band anti-crossing (BAC) k ∙ p model for N-rich alloys. This model captures the reduction of bandgap with increasing arsenic incorporation and provides a tool for device-level design with the material within the context of the k ∙ p formalism. The analysis extends to calculating the effect of the arsenic impurities on hole (heavy, light and split-off) effective masses and predicting the trend of the bandgap across the entire composition range.