This doctoral thesis presents a physically non–linear adaptive Finite Element Method which
enables the analysis of reinforced concrete panels in a state of plane stress. The material model is an elastic–plastic one. The yield surface which is related to plain concrete consists of different yield criteria. A special method of composing the different criteria provides unique derivatives of the yield function with respect to the stress vector in any point of the yield surface. The application of special error indicators, which are adjusted to the present material model, enable an automatic control of the size of the incremental load steps and an automatic adaptive mesh refinement. Various numerical examples demonstrate the efficiency of the model.