A constitutive equation for elasto-plastic damageable solids is formulated by using Drucker-Prager's equivalent stress to analyze the damage failure behavior of concrete structural elements reinforced with carbon fiber sheets. The forumulated constitutive equation is implemented in the two-dimensional finite element program to simulate the experimental results. The constitutive equation is identified by using the uniaxial, compressive and tensile test results for concrete and carbon fiber sheets. The finite element analyses are carried out for real-scaled cantilever RC slabs with and without carbon fiber sheets. The calculated results are compared with the experimental results to illustrate the validity of the proposed method of analysis.