In this chapter, we explore how fault hydromechanical behavior can impact seismic rupture. Our focus is to describe how an initially inactive fault hidden in a basin can be activated by CO2 injections. Moreover, we explore if there is any parameter specific to CO2 storage that has to be considered in induced seismicity. In Sect. 4.1, we first describe the most current framework used to define fault plastic instability which is based on the rate-and-state friction model. Second, we describe an alternative concept based on “standard” plasticity (Piau et al. in J Geophys Res Solid Earth, 125, 2020). We discuss how this alternative model may me more general than the rate-and-state friction model. In Sect. 4.2, we describe how the rate-and-state friction physics has been implemented into fluid injection numerical models and applied to describe induced seismicity at basin scales. Section 4.3 is an attempt to define some specificities of seismicity induced by CO2 storage. In Sect. 4.4, we test the effects of some CO2 injection specificities using the “standard” plasticity model from Piau et al. (J Geophys Res Solid Earth, 125, 2020). We highlight the possible strong influence of the brine compressibility evolution with CO2 saturation on fault seismic rupture.