Remember Bob you can blast/peen a mild steel workpiece with stainless shot ok but if you blast a stainless one with mild steel shot you will get rust.
Peening puts stress into the material surface so don't let anyone go wild with high energy shot media, or you could end up with a bent bang stick pipe! Best go with glass bead at lower pressure, however that won't take out heavy surface blemishes or dings.(Polish them out before blasting).
Any blasting of a barrel should be done with the workpiece rotating to impart even stress all round the diameter, exposing all the surface area to the same amount of blasting by feeding the nozzle steadily up the length (same as a lathe tool).
Ian