When I add a cylinder in blender and then add a subdivision surface the vertices of the cylinder get all rigid and pointy. How do I make the cylinder have smooth faces when using the subdivision surface modifier without it making the vertices rigid. I want the cylinder to be smooth so I can model something like a cup. Even after I add the subdivision surface and then put smooth shading the vertices are still rigid and pointy and even when I subdivide it as well.
To subdivide a cylinder with a Subsurf modifier, you'll need to add holding edges to where you want the edges to be sharp. This can be achieved by using the bevel tool.
While in edit mode, Alt-select the edges that you would like to be sharp, then press Ctrl-B to set a bevel width. I set the amount of Segments to '2' and a Profile of '1' so that if I need to remove my holding edges, my original edge will be where I originally had it before beveling.
Use shading smooth and an edge split modifier and use high vertex density. No Subdivision Surface was used below. At this simple stage you may decide it unnecesary. Feel free to delete your current cylinder and have a fresh start. Below are cylinders with different vertex density values selected at creation time.
Below closeup of active edge split.
Below closeup of disabled edge split.
You can increase vertex density as indicated below.