Mathias Ham House is an example of a large, antebellum residential architecture reflecting an eclectic architectural style. The contrasts between the earlier and later sections of the structure show the improving fortunes of Mathias Ham, an early Dubuque settler who was a farmer, lumberman, brick maker and shipper, as well as being socially and politically active. The mid-Victorian house brings together a variety of architectural influences in a building of cleanly-dressed ashlar. The side porch with its Tudor style wooden arches supported by octagonal columns is painted white. The Tudor arch is repeated on the front porch flanked by narrower rounded arches of Romanesque style. The large portion of the structure is actually a later addition in 1857 to the much simpler farmhouse constructed in 1839.