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The paper presents the procedure for determining the factor of safety (FoS) using the strength reduction method (SRM) for the case of a concrete damage plasticity constitutive model. The SRM was originally used in a slope stability analysis and in its original form, this method was applied by reducing the shear strength of the material. Since damage in concrete occurs due to exceeding the normal stresses in the principal directions, and not due to exceeding the shear strength, this method was modified and adapted to the concrete damage plasticity constitutive model. Instead of reducing the failure surface, the parameters which describe the mechanical behavior in the case of uniaxial compression and uniaxial tension were reduced. In this way, the reduction of stress and the corresponding strain was carried out in the entire range of total strain, without changing the shape of the failure surface in the deviator plane. For the proposed methodology, a numerical algorithm was developed and implemented into the software PAK. The algorithm was verified through test examples and the obtained results were compared with analytically calculated FoS. The excellent agreement is observed between the FoS obtained by applying the proposed algorithm and the analytically calculated FoS. [ABSTRACT FROM AUTHOR]