To make meat more tender to eat, carve roast beef across the grain (i.e. across the muscle fibres). Cutting across the muscle fibres shortens them. The more you shorten the long muscle fibres (i.e. the thinner the slice), the more tender the meat will seem.
Tip: Carving in the same direction as the butcher’s twine should be across the grain if your butcher did the cutting right.