A pebbling move on a graph
G
consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the strict rubbling move. In this new move, one pebble each is removed from
u
and
v
adjacent to a vertex
w
, and one pebble is added on
w
. The rubbling number of a graph
G
is the smallest number
m
, such that one pebble can be moved to each vertex from every distribution with
m
pebbles. The optimal rubbling number of a graph
G
is the smallest number
m
, such that one pebble can be moved to each vertex from some distribution with
m
pebbles. In this paper, we give short proofs to determine the rubbling number of cycles and the optimal rubbling number of paths, cycles, and the grid
P
2
×
P
n
; moreover, we give an upper bound of the optimal rubbling number of
P
m
×
P
n
.