Extra facet generation during molecular beam epitaxy of GaAs/AlGaAs multilayers on (001) GaAs substrates patterned with stripes running in the [<(1)over bar 10>], [110], and [100] directions and having various slopes, designated as "[<(1)over bar 10>] stripe," "[110] stripe," and "[100] stripe," respectively, has systematically been investigated for the first time. It has been confirmed that extra (111)A and (114)A facets are generated on the [<(1)over bar 10>] stripes, extra (<(1)over bar 11>)B and (<(1)over bar 13>)B facets on the [110] stripes, and extra (031), (011), (045), and (013) facets on the [100] stripes, depending on the intersection angle theta of the sidewall and the substrate plane. Among them, the (114)A, (<(1)over bar 13>)B, and (013) facets are important because they persist over a wide range of theta and, therefore play a detrimental role in forming flat and uniform sidewall layers on the (001) patterned substrates. It has been made clear that no extra facets are generated on the sidewalls and flat and uniform layers maintaining the initial as-etched stripe patterns can be grown for the [<(1)over bar 10>] stripes with 10 degrees greater than or equal to theta, the [110] stripes with 24 degrees greater than or equal to theta greater than or equal to 20 degrees, and the [100] stripes with 19 degrees greater than or equal to theta. Extra (111)A-related facets have developed on the (111)A-related intersection of the equivalent [100] and [010] stripes, while no extra facets have developed on the (<(1)over bar 11>)B-related intersection. The facet generation behavior has been compared between the (001) patterned substrates and previously studied (111)A patterned substrates.