Paper and paperboard are gaining importance in many engineering applications, in particular in the packaging industry, since they are sustainable materials that are extremely versatile, renewable, and easily recyclable. This leads to the demand for simulation tools to predict the material response. However, the modeling of paper and paperboard is rather challenging due to the complex material behavior. Paper and paperboard are anisotropic resulting from the manufacturing process. In particular, three preferential material directions can be defined: machine direction (MD), cross direction (CD), and out-of-plane direction (ZD) (cf. [1]). As shown experimentally in [2], the out-of-plane response is independent of the in-plane (MD and CD) one. Thus, a decoupled material behavior in in-plane and out-of-plane directions can be assumed. In addition to this anisotropy, a challenge in modeling the material behavior lies in the nonlinear mechanical response defined by, for example, elasto-plasticity and damage. However, these have not been investigated sufficiently so far. Therefore, the aim of this work is to present a continuum mechanical model that captures the anisotropic damage progression in paper and paperboard. For this, the anisotropic structure is incorporated by use of structural tensors, which are aligned with the preferential material directions. In addition, a split of the deformation into in-plane and out-of-plane contributions is applied. Finally, the models capabilities to present the mechanical response of paper and paperboard are demonstrated by numerical examples.