The formation of ordered InAs/InP quantum dot (QD) arrays is demonstrated on patterned InP (1 0 0) and (3 1 1)B substrates by the concept of self-organized anisotropic strain engineering in chemical beam epitaxy (CBE). On shallow- and deep stripe-patterned InP (1 0 0) substrates, depending on the stripe orientation, the linear one-dimensional InAs QD arrays are rotated away from their natural direction due to the presence of vicinal stepped sidewall planes modifying the self-organization process, coexisting with QD free steep side facets on the deep-patterned substrates. On shallow- and deep-patterned InP (3 1 1)B substrates only QD free side facets form with flat top and bottom areas, not affecting the natural ordering of the two-dimension...