A surface winder having an undercut drive roller. An apparatus for winding web material onto a core includes a driven pressure roller having a first end portion, a second end portion, and a central portion intermediate the first and second end portions. When the pressure roller is driven against the core, a first and second nip is formed between the first and second end portions, respectively, and the core. The central portion is undercut so as to space the central portion from the web material being wound onto the core.