The disposal of mining tailings has increasingly focused on the use of dry stacks. These structures offer more security since they use filtered and compacted material. Because of the construction method and the heights achieved, the material that compounds the structure can be subjected to different stress paths along the failure plane. The theoretical framework considered in the design of these structures generally is the critical state soil mechanics (CSSM). However, the data in the literature concerning the uniqueness of critical state line (CSL) is still controversial as the soil is subjected to different stress paths. With respect to tailings, this question is even more restricted. This paper studies two tailings with different gradings due to the beneficial processes over extension and compression paths. A series of drained and undrained triaxial tests was conducted over a range of initial densities and stress levels. In the q-p' plane, different critical stress ratio (M) values were obtained for compression and extension stress paths. However, the critical state friction angle is very similar with a slightly higher critical state friction angle for extension tests. Curved stress path dependent CSLs were obtained in the ν-lnp' plane with the extension tests below the CSL defined in compression. Regarding the fines content, the studied tailings presented very similar M and critical state friction angle values. However, the fines content affects the volumetric behavior of the studied tailings and the CSLs on the ν-ln p' plane shift downwards with the increasing fines content for compression and extension tests. In relation to dilatancy analysis, the fines content did not present an evident influence on the dilatancy of the materials. However, different values of mean stress ratio N were obtained between compression and extension tests and can corroborate the existence of non-unique CSLs for these materials.