Various carbon nanostructures and their properties are of great interest nowadays. It is well known that graphene has unique mechanical properties among other carbon nanomaterials and at some conditions graphene can show auxetic behavior which means that it can have negative Poisson’s ratio. From the consideration of the mechanical properties of graphene and 3D carbon-based nanomaterials, several groups of promising candidates to be auxetics can be mentioned. In this study, mechanical properties of strained graphene and different diamond-like three-dimensional structures based on carbon nanotubes (tubulanes) are investigated by molecular dynamics method. It is shown that graphene has negative Poisson’s ratio under homogeneous tensile strain above 0.12. It is found that three of the studied tubulanes have negative Poisson’s ratio.