One widely used measure of genetic similarity for pairs of relatives is gene identity-by-descent (IBD) sharing. Genes that are copies of a single gene in a common ancestor of the individuals who now carry them are said to be IBD. One obvious extension of the IBD concept is IBD gene(s) shared by more than two individuals. In this paper, I further extend the gene IBD concept to the proportion of genomes shared IBD by every member of a group of relatives. Genome may refer either to the entire autosomal genome or to one or more chromosomal segments or regions with known lengths. Consideration of a genome instead of one or two loci has several advantages. I present a model to describe the crossover process, based on the work of K. P. Donnelly. On the basis of this model, I give a mathematical definition of the proportion of genome shared IBD by relatives, or IBDP for short. Since the distribution of the IBDP is in general very difficult to determine, and since in most applications the mean and variance of the IBDP will suffice, I then provide a method for computing the first two moments of the IBDP. Applications to assessing gene survival, to genetic resemblance between two relatives, and to gene mapping are illustrated with examples. Finally, I discuss the utility of the IBDP in other areas.