The most common 1950s asbestos siding is a cement product often embrossed with a wood grain or split cedar appearance. It is roughtly 3/16" thick and is very tough. When broken it can produce dust and may have visible fiber. A $25 test using polarized light microscopy (PLM) can tell definitively if it is asbestos-containing (look under Laboratories Analytical in the Yellow pages).
I have applied vinyl siding over the top of the material, but it is so tough, you have to pre-punch the nail holes. Use reasonable precautions to prevent personal exposure (HEPA cartrige respirator and spray bottle to suppress dust). Contact your local building department regarding legal issues, but in most places, only removal is regulated.