The equilibrium structure of the semi-infinite, one-dimensional stepping-stone model is investigated in the diffusion approximation. The monoecious, diploid population is subdivided into a semi-infinite linear array of equally large, panmictic colonies that exchange gametes uniformly and symmetrically. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to new alleles at the same rate. Boundaries corresponding to an impenetrable geographical barrier and to contact with a region of extremely high population density or dispersal rate (a “density-mobility boundary”) are both treated. Relative to a homogeneous infinite habitat, a geographical barrier raises, and a density-mobility boundary lowers, the probability of identity. For fixed average position of the two points of observation, the probability of identity decreases with increasing separation. For fixed separation, the probability of identity decreases (increases) as the average position recedes from the barrier (density-mobility boundary). The sole dimensionless parameter in the theory is β = 4 ρo √2 uV o , where ρ o , u, and V o represent the population density, mutation rate, and variance of gametic dispersion per generation, respectively. The characteristic length is √ V o (2u) . Lower and upper bounds on the probability of identity are established; these yield a simple approximation for β ⪢ 1. The probability of identity is obtained as an integral; from this solution, approximations close to and far from the boundary are derived and the exact mean homozygosity at a geographical barrier is evaluated.