The influence of capillarity on the near-plane front solidification of metal matrix composites is examined by analysis of the one-sided solidification of a binary alloy in a planar interstice of constant width in the limit of low Peclet number. We assume that in this limit, solute isoconcentrates in the liquid are everywhere orthogonal to the growth direction. Capillarity causes the alloy to solidify in a cellular mode, even in the absence of constitutional supercooling. Two solution branches are derived for this solidification mode, one for shallow symmetric cells, the other for asymmetric cells. Restricting attention to the former solution branch, as the growth velocity increases, or the temperature gradient decreases, the cell amplitude increases gradually, to reach a critical point which depends strongly on the contact angle along the reinforcement/solidification front triple line. Copyright (C) 1996 Acta Metallurgica Inc.