Self-assembly of block copolymers in the presence of solvents forms ordered mesophase structures, also known as lyotropic liquid crystals (LLCs). The aim of this work is to investigate the rheological properties of Pluronic block copolymer/water/oil mesophases with lamellar and hexagonal structures. The flow behavior of lamellar and hexagonal mesophases indicates that they have yield stress. Oscillatory shear experiments show that mesophases have solid-like behavior and exhibit type III non-linear behavior. The elastic modulus of mesophases is probably controlled by the van der Waals interaction between micelles. We suggest that at relatively low frequencies, defects control the rheological behavior of LLCs, while at high frequencies, the contributions in micellar scale are dominant. Applying high strains on the LLCs induces two relaxation times after cessation of flow, decreases the storage modulus in the whole frequency range, and decreases the loss modulus in small-frequency regime with negligible effect at high frequencies. The decrease in moduli is reversible and the system relaxes back to its original elastic modulus at rest. The observed behavior can be attributed to the elimination of defects under high strains and their re-formation during long enough rest times.