If you have a photo of it, you can Google "vintage Singer sewing machine" and then click on "images". Try to match the machine to one of the vintage photos to find out the model number.
What kind of Singer case does it come with? Is it the "portable" type with a curved wooden dome top?
What I'm wondering is if it might be some kind of replica or reproduction model. Those can be not very good because they were not machined to the same exacting specifications as the originals.