Covering the entire block bounded by Ohio, Meridian, New York, and Pennsylvania Streets, the United States Court House and Post Office Building was the first and largest local example of the monumental Beaux-Arts style, a type of neoclassicism that became popular nationally in the wake of the World's Columbian Exhibition in Chicago. This style is used for many US government buildings, as well as other prominent civic structures such as art museums, across America. The Court House anchors the southern end of the seven block war memorial mall, a grand City Beautiful space that is amongst the finest in America.

Elements of the Beaux-Art style include classical detailing, grand entrances to elevated first floors, symmetry, flat roots, the use of statuary, and luxurious materials. It was named after the Ecole de Beaux-Arts, or School of Fine Arts, in Paris where it was taught.

The Court House was built from 1902 to 1905 at a cost of nearly $2 million. It originally housed not just federal courts, but all federal functions including the main Post Office. In fact, the post office continued to be based at this building until 1973. Most other federal offices are now housed elsewhere, and this is primarily a court house. The original building was actually U-shaped, but the court yard was full enclosed during an 1838 expansion of the building.

The interior features extensive and ornate murals and art work, as well as lavish finishings. The building is open to the public, but since it is a court house, enhanced security screenings are in effect, so please verify restrictions prior to entering.

The Court House was named in honor of former US Senator Birch Bayh, father to current US Senator Evan Bayh, in 2003. It is on the National Register of Historic Places.