Octopus suckers are able to attach to all nonporous surfaces and generate a very strong attachment force. The well-known attachment features of this animal result from the softness of the sucker tissues and the surface morphology of the portion of the sucker that is in contact with objects or substrates. Unlike artificial suction cups, octopus suckers are characterized by a series of radial grooves that increase the area subjected to pressure reduction during attachment. In this study, we constructed artificial suction cups with different surface geometries and tested their attachment performances using a pull-off setup. First, smooth suction cups were obtained for casting; then, sucker surfaces were engraved with a laser cutter. As expected, for all the tested cases, the engraving treatment enhanced the attachment performance of the elastomeric suction cups compared with that of the smooth versions. Moreover, the results indicated that the surface geometry with the best attachment performance was the geometry most similar to octopus sucker morphology. The results obtained in this work can be utilized to design artificial suction cups with higher wet attachment performance.