In the present work, the mechanical behavior of stress corrosion cracking phenomenon is described. Such phenomenon presents strong complexity due to metallurgic and electrochemical aspects. A methodology for modeling both SSR (Slow Strain Rate) and CL (Constant Load) tests based upon thermodynamics of continuum solids and elastoplastic damage is proposed. In this macroscopic approach, besides the classical variables (stress, total strain, plastic strain), an additional scalar variable related to the damage induced by stress corrosion is introduced. An evolution law depending on the corrosive environment parameters is proposed for this damage variable. The model accounts for the stress corrosion effect through a reduction of the mechanical resistance of the material induced by the damage variable. The model prediction is compared with the curves obtained experimentally in different acid solutions at room temperature showing a good agreement. The alloy/environment system studied here is an AISI 304 austenitic stainless steel in acid aqueous solution containing sodium chloride.