The authors consider rate splitting and interference cancelation in Device-To-Device (D2D) communications underlaying a cellular network. They assume that a transmitted message is split into a private and a public part, as in Han-Kobayashi scheme. The private part is decodable only by the intended receiver, whereas the public part is in addition decodable by an interference victim. The receivers run a best-effort Successive Interference Cancelation (SIC) algorithm, canceling interfering public signals. They derive the optimal rate splitting factors for most of the categorized channel conditions in a two-link scenario. They use the rate splitting scheme for resource sharing in a two-link D2D underlay cellular network.