In his fundamental book Nielsen (1984) summarized the basics of application of plastic theories to the design of concrete structures. Since that time extended experimental and theoretical works were carried out. Models based on plastic theories were developed for bending, shear, for beams, plates, etc. The strut-andtie-, the stress field models and the Modified Compression Field Theory perform further developments of application of the theory of plasticity. Crucial point (the governing material characteristic) of these models is the effective concrete compressive strength. This paper critically reviews its different theoretical origins and despairs of its existence. It reveals that the main source of plastic behavior of structural concrete structures is the reinforcement. In design for shear instead of a preposterous effective concrete strength the effective web thickness and (a maybe slightly reduced) concrete compressive strength should be taken into account. Neither the concrete compressive strength nor any reduced (effective) value of it are applicable as governing material characteristic of any plasticity model for structural concrete structures.