The rheological and morphological properties were examined on solutions of a styrene‐butadiene (SB) diblock copolymer in so‐called selective solvents, which dissolve only one block but precipitate the other. In such solvents the block copolymer molecules aggregate and form micelles with the precipitated blocks as the cores and the dissolved blocks as the cilia. Above a certain critical concentration and below a certain critical temperature, the solutions exhibit nonlinear behavior even under small‐amplitude oscillation and also plastic flow with a true yield stress. A simple constitutive model incorporating the plasticity as well as the viscoelasticity describes these plastic and nonlinear behavior, at least, semiquantitatively. Small‐angle x‐ray scattering studies on these solutions indicate that the block copolymermicelles are regularly arranged into a simple cubic “macrolattice.” The micellar solutions undergo a transition from plastic, nonlinear behavior to linear viscoelastic behavior, either with increasing temperature or decreasing concentration, accompanied by a transition from the ordered macrolattice structure to a disordered structure in which the micellles are dispersed randomly. These results suggest that the stability of the macrolattice is the main cause of the plasticity of the solutions. The nature of the plasticity is discussed in terms of density fluctuation of the ciliary block chains within the macrolattice space.