Using a multiscale approach, the critical compressive load of a cylindrical shell made by concrete/graphene nanocomposite is computed. At the first step, using a multiscale method, the elastic modulus of concrete/graphene nanocomposites with different graphene volume percentages and sizes are evaluated. Then, the finite element method is used to obtain the critical compressive load of a cylindrical shell made by the concrete/graphene nanocomposites. It is observed that the elastic modulus and buckling load of the concrete/graphene nanocomposites are reduced by increasing the temperature. It is also shown that when the graphene sheets are directed along the external force, the mechanical properties of the concrete are improved more than the case in which the graphene sheets are randomly directed in the concrete matrix.