The non-rotating cementing plugs significantly reduce the drill out time, which leads to high efficient and cost saving. The cup design on top and bottom of both plugs provides a sure seal against the casing wall to prevent mixing of cement slurry and displacement fluid. The top plug seats into the bottom Plug and seals against it to lessen the possibility of additional cement slurry displacement, while also promoting good bonding at the bottom of the casing. No metal parts are used, so the plugs are competely PDC drillable.