Shear stress growth and relaxation behavior of two well-characterized SBS block copolymers have been studied using a Melt Elasticity Tester. Effects of casting solvents on the transient rheological properties and structure variation during flow are determined via samples cast from THF/MEK and cyclohexane. The temperature dependence of the observed shear stress at the yield point and steady-state viscosities provides insight into the mechanism of structure breakdown induced by the applied flow. Shear stress relaxation upon cessation of flow reveals complex behavior, depending on temperature, casting solvents, and duration of previous flow. Strain recovery data have also been obtained, indicating strong dependence on the composition of the copolymers. Significance of these observations in terms of the melt structure of SBS is discussed.