If you can see the tub from underneath and it looks black it is probably cast iron. If it is more like bright metal it is steel. If you want, remove the overflow cover and popup lever from the head end of the tub and look at the edge of the hole. You should see black cast iron or bright steel. You could also rap your knuckles on one of your wife's metal mixing bowls and note the sound. (steel) Then if she has a black castiron skillet, do the same thing again. Note the sound.(cast iron) Now go rap on the long side wall of your tub. (Cast iron or Steel?)