Stellar streams originating in disrupted dwarf galaxies and star clusters are observed around the Milky Way and nearby galaxies. Such substructures are the important tracers that record how the host halos have accreted progenitor galaxies. Based on the cosmological context, we investigate the relationship between structural properties of substructures such as length and thinness at z = 0, and orbits of their progenitors. We model stellar components of a large sample of substructures around Milky Way-sized halos by combining semi-analytic models with a high-resolution cosmological N-body simulation. We find that the length and thinness of substructures vary smoothly as the redshift when the host halos accrete their progenitors. For substructures observed like streams at z = 0, a large part of the progenitors is accreted by their host halos at redshift 0.5 < z < 2.5. We also find that the distributions of length and thinness of substructures vary smoothly as pericenter and apocenter of the progenitors.