The quantum chemical simulation of adsorption of atomic hydrogen on pristine and nitrogen-doped graphdienes has been performed. The preferential sites, adsorption on which is most energetically beneficial, are indicated. The nitrogen presence is shown to substantially increase the adsorption capacity of the sheet. A capacity of the nitrogen-doped graphdiene to be reversibly stretched by 4% under action of external mechanical stress is demonstrated. A mechanical stretching is found to enable the control of the adsorption properties of pristine and also doped graphdienes.