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The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that,however $p$ pebbles are placed on the vertices of $G$, we can move a pebble toany vertex by a sequence of moves, each move taking two pebbles off one vertexand placing one on an adjacent vertex. It is conjectured that for all graphs$G$ and $H$, $f(G\times H)\leq f(G)f(H)$. If the graph $G$ satisfies the oddtwo-pebbling property, we will prove that $f(C_{4k+3}\times G)\leqf(C_{4k+3})f(G)$ and $f(M(C_{2n})\times G)\leq f(M(C_{2n}))f(G)$, where$C_{4k+3}$ is the odd cycle of order $4k+3$ and $M(C_{2n})$ is the middle graphof the even cycle $C_{2n}$.

Pebbling on $C_{4k+3}\times G$ and $M(C_{2n})\times G$