The Target Development Facility (TDF) reaction chamber will be subjected to a mechanical shock from the cavity gas after each target ignition. This impulsive pressure produces transient stresses in the cylindrical shell wall which are characterized by an oscillatory response with decreasing amplitude. Such fluctuating stresses may fatigue the wall material and limit the useful lifetime of the chamber. Lifetime estimates have been determined and comparisons are made for chambers with different sizes, alloys and target yield.