sewingmachine that can sew leather/pleather

What do you mean by 'very old'? If it's one of the older black cast iron bodies, it'll sew garment leather just fine. You might need to adjust tension and presser foot pressure, and may need leather needles (though some folk use sharps/jeans needles successfully). You'll want decent thread suitable for the purpose.

Basic, but worth asking: did you remember to fill and load a bobbin (correctly), and to thread the upper thread properly through the tension disks, take-up lever, and all the guides?

Sounds like the machine will feed leather just fine, and that the needle penetrates your leather as well, so maybe you have a threading problem? Double check that the bobbin and needle threads are threaded properly, and test the tension on some scraps. There are diagrams for threading many machines here:

Beverly

I use denim sharps with leather, not the leather needle that leaves holes where I've stitched. I have 1n 1898 Singer-don't remember the, but it sews great stitches but has to adjusted for leather. Emily

Do not use leather needles. You will end up with large slices in the leather. Usually when your results are like this its a feed problem. Try a Teflon foot, and also some kind of underlay to keep the leather moving freely on the machine bed. Most problems are caused by the leather either sticking to the machine or the foot. I use sharp needles no larger than 16 for all leather, and I do a lot of it for Native American Regalia......mostly deer and moose hides which can be quite thick. A good cotton wrapped poly or nylon thread is a preferred choice. Please stay away from Leather needles, any machine will sew leather. Some for longer than others but any machine can do it.