The 'RETICOLOfilm-stack' program is a free software operating under Matlab. It computes the reflection and transmission of arbitrary stacks of anisotropic thin films. The present hal-document is the documentation. RETICOLOfilm-stack is related to another freeware, RETICOLO [arXiv:2101.00901], which analyzes the diffraction by gratings with the Rigorous Coupled Wave Analysis. The version V9 of RETICOLO discusses the possibility of analysing thin-film stacks, simply by retaining a single component of the RCWA Fourier extension. However, it is not optimized in computation time, because loops for scanning the wavelengths and incidences have to be implemented. RETICOLOfilm-stack is vectorialized and thus treats several wavelengths and incidences in a single instruction. Compared to the state of the art, see Section XI.2 of the present document, RETICOLOfilm-stack appears highly reliable, effective and general. We expect that it may thus be useful. To install the software, download it from zenodo (https://doi.org/10.5281/zenodo.7429031) and add the downloaded folder in the Matlab path.