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The continuum damage mechanics-based elasto-plastic damage theory, that extends the total form of Hayakawa and Murakami equations, is developed. Weak elastic-plastic dissipation coupling is assumed by the use of two dissipation potentials, plastic and damage, where only isotropic plasticity and damage hardening is included, whereas kinematic hardening is not accounted for. Unilateral damage condition, based on the concept of generalized projection operators, accounts for a partial damage deactivation, which allows for an influence of negative principal components of the stress tensor on damage evolution. The incremental representation of the elastic-damage constitutive equations is derived. Both elastic-damage and plastic-damage compliance matrices are developed for plane stress condition, and implemented to ABAQUS finite element code by the user-supplied procedure for non-standard material properties. Effective computation algorithm for plastic and damage loading/unloading conditions based on the doubly passive predictor and plastic-damage corrector approach is proposed. Numerical examples are presented by applying the model calibration by Hayakawa and Murakami for the spheroidized graphite cast iron FCD400. The examples illustrate the capability of the model to describe elastic-plastic damage evolution under monotonic loading. Under reverse loading conditions a partial elastic stiffness recovery was demonstrated on the consecutive increasing strain-controlled loading cycles and some limitation of the model was shown. [ABSTRACT FROM AUTHOR]