The model # is a bit more difficult to determine. You'll need to look at pictures and compare features of your machine to them.
Knowing the year of manufacturer is one step. Then you look at the stitch length control, is it a small knob that moves up and down, or a nice lever in a circular disk held on by two tiny screws.
Here is another link that "might" help some more:
{
http://www.ismacs.net/singer_sewing_...ist/index.html }
You might also post some pics of it, others that know them by sight could help then.
Joe