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In the study of blast waves from a finite sphere, it has been observed that in addition to the primary strong shock wave ahead of the driving gas, a second shock also forms inside of this driving gas. This formation of the second shock will invalidate all the existing theories of blast waves in that an additional non-isentropic region actually exists inside of the interface between the driven and the driving gas. This thesis investigates the behavior of this second shock and the resultant flow patterns.