Recently hybridized monolayers consisting of hexagonal boron nitride (h-BN) phases inside graphene layer have been synthesized and shown to be an effective way of opening band gap in graphene monolayers [1]. In this letter, we report an ab initio density functional theory (DFT)- based study of h-BN domain size effect on the elastic properties of graphene/boron nitride hybrid monolayers (h-BNC). We found both inplane stiffness and longitudinal sound velocity of h-BNC linearly decrease with h-BN concentration.