The INFN CNAF Tier-1 has become the Italian national data center for the INFN computing activities since 2005. As one of the reference sites for data storage and computing provider in the High Energy Physics (HEP) community it offers resources to all the four LHC experiments and many other HEP and non-HEP collaborations. The CDF experiment has used the INFN Tier-1 resources for many years and, after the end of data taking in 2011, it faced the challenge to both preserve the large amount of scientific data produced and give the possibility to access and reuse the whole information in the future using the specific computing model. For this reason starting from the end of 2012 the CDF Italian collaboration, together with the INFN CNAF and Fermilab (FNAL), introduced a Long Term Data Preservation (LTDP) project at our Tier-1 with the purpose of preserve and share all the CDF data and the related analysis framework and knowledge. This is particularly challenging since part of the software releases is no longer supported and the amount of data to be preserved is rather large. The first objective of the collaboration was the copy of all the CDF RUN-2 raw data and user level ntuples (about 4 PB) from FNAL to the INFN CNAF tape library backend using a dedicated network link. This task was successfully accomplished during the last years and, in addition, a system for implementing regular integrity check of data has been developed. This system ensures that all the data are completely accessible and it can automatically retrieve an identical copy of problematic or corrupted file from the original dataset at FNAL. The setup of a dedicated software framework which allows users to access and analyze the data with the complete CDF analysis chain was also carried out with detailed users and system administrators documentation for the long-term future. Furthermore a second and more ambitious objective emerged during 2016 with a feasibility study for reading the first CDF RUN-1 dataset now stored as an unique copy in a huge amount (about 4000) of old Exabyte tape cartridges. With the installation of compatible refurbished tape drive autoloaders an initial test bed was completed and the first phase of the Exabyte tapes reading activity started. In the present article, we will illustrate the state of the art of the LTDP project with a particular attention to the technical solutions adopted in order to store and maintain the CDF data and the analysis framework and to overcome the issues that have arisen during the recent activities. The CDF model could also prove useful for designing new data preservation projects for other experiments or use cases.