Related individuals are identical by descent (IBD) at a genetic locus if they share the same DNA material from a common ancestor. Continuous gamete IBD data consist of the lengths of (in order) IBD and non-IBD regions along the genomes for gametes segregating from two related individuals and can be used to distinguish different relationships. Under the assumption that the crossovers follow a Poisson process, we show that the exact calculation of the likelihood of a particular relationship for a given gamete IBD datum is tractable. Greatgrandparent--greatgrandchild and cousin relationships are used as examples to illustrate our methods.