Bill, "with the grain" is slicing lengthwise, in line with the muscle fibers. Against the grain is 90-degrees perpendicular to the grain. If you look at a brisket, the grain is very pronounced, usually diagonal across the flat. That's why you slice brisket at an angle that is 90-degrees off the grain - it makes the slices very tender. When I make beef jerky, I slice with the grain, so it's long fibers the length of the slices. I'll try and find some pics to better illustrate this.