We study the isoperimetric problem in the Riemannian products S-1(r) x Q(c)(n), where Q(c)(n) is the n-dimensional simply connected space form of constant sectional curvature c = 0, 1, -1, and r > 0. The problem of classifying stable free boundary hypersurfaces with constant mean curvature between two parallel hyperplanes in R-n for n greater than or equal to 3 is also treated.48413571394