Through continuum elasticity we define a simulation protocol addressed to measure by a computational experiment the linear elastic moduli of hydrogenated graphene and we actually compute them by first principles. We argue that hydrogenation generally leads to a much smaller longitudinal extension upon loading than the one calculated for ideal graphene. Nevertheless, the corresponding Young modulus shows minor variations as function of coverage. Furthermore, we pThrough continuum elasticity we define a simulation protocol addressed to measure by a computational experiment the linear elastic moduli of hydrogenated graphene and we actually compute them by first principles. We argue that hydrogenation generally leads to a much smaller longitudinal extension upon loading than the one calculated for ideal graphene. Nevertheless, the corresponding Young modulus shows minor variations as function of coverage. Furthermore, we provide evidence that hydrogenation only marginally affects the Poisson ratio.