The U.S. Army never issued a drinking cup.  Some vendors have named the product they sell the "1851 regulation cup M1851", but there are no military regulations.  Drinking cups were either issued by states as with the New York Militia or by groups such as the U.S. Sanitary Commission.  There are many extant cups from the Civil War but it is difficult to determine which cup was the most prevalent.  I was able to identify 3 cups that had identical features and that is the cup I make. 

I cut out the body, handle and circle for the bottom then shape the parts on the original pre Civil War Machines.

The body is bent on the bar folder and a tube is formed.  The seam is grooved on the grooving machine made by Roys & Wilcox who started in 1843 in East Berlin CT.

The lip is turned over on the turning machine made by Peck Smith Mfg Company.  This is the 1859 Raymond patent machine.

A wire is inserted to make the top of the cup stronger and to prevent one from cutting their lip.  The wiring machine curves the tin around the wire.  I use an S. Stow Co machine made in Southington CT between 1851 and 1853.

I cut out a circle on the 1860 patent  J. Waugh Circle cutter.

The circle is burred on the S. Stow machine made after they moved to Plantsville CT in 1853.

The bottom is attached to the side with a set down seam.  The sides are burred out and the bottom is burred up and back over and then is "smashed" down using the S. Stow setting down machine manufactured in Plantsville CT.  The plant opened in 1853.

The bottom is double seamed on a W. Burton patented June 21, 1859.  Double seaming the bottom makes it so that soldering is not required to make the cup hold liquid.  Where the vertical seam meets the bottom does require some solder as a gap is formed.  The soldered "T" is found on most original double seamed cups.

The handle is cut out and folded over on the the Bar Folder.  The Roys & Wilcox name and S. Stow name both appear on the Bar Folders from the period. This device for breaking was advertised as early as 1820 in the Connecticut Current.

The wire is inserted in the fold and run through the wiring machine.  The wire is wrapped around the rim of the cup.

The handle is not centered on the seam as is seen in most reproduction cups. A rivet is added to the base of the handle.  A disc is added for strength between the handle and the rivet.  I have never observed this feature on any reproduction cups. The wire at the top and rivet help prevent the handle from coming off if the cup is over heated.

And the cup is ready for use.