A rubber pad construction is adapted for use in making a shoe sole, a shoe pad, a face layer of a table-tennis paddle, a shell of a ball, etc. The rubber pad construction includes a substrate, and a plurality of first and second protrusions which extend outwardly from one side of the substrate at intervals. The first protrusions are thinner and higher than the second protrusions to provide more flexibility. The second protrusions have more bearing ability than the first protrusions. The rubber pad construction provides desirable shock-absorbing and rebounding qualities.