A fundamental set of issues in human genetics research concerns the statistical properties of the DNA sequence or chromosomal segments that are shared between related individuals. Although well-established mathematical formulations exist that consider such sharing via measures such as the kinship coefficient, many of these formulations are derived for entire genomes, individual sequence variations, or small stretches of DNA, and hence, do not consider either the actual size or the number of the genome-wide chromosomal segments that are shared between two or more arbitrarily related individuals. In this paper, we employ a flexible gene-dropping simulation-based approach for estimating the distribution of the size and the number of chromosomal segments shared by any number of arbitrarily related individuals. The approach takes advantage of chromosome- and sex-specific recombination rates adopted from integrated genetic and physical maps, and considers the genome as a whole, rather than specific genomic regions or loci. In addition, our analysis considers the effects of linkage disequilibrium and crossover interference on segment sharing. Our proposed analysis and computational strategy can be used to provide compelling answers to questions concerning variation in the kinship coefficient as well as the distribution of chromosomal sharing over individual chromosomes. We present results that showcase possible application of assessing genomic sharing in gene mapping and apply our analysis to data available from published gene mapping studies.