Insignia Description
A Silver metal and enamel device 1 1/8 inches (2.86 cm) in height consisting of a shield blazoned: Argent, a patriarchal cross botonny Azure between in fess debased an oak tree Vert and a lion rampant Sable. Attached below and on the sides of the shield, a Blue scroll inscribed "DUCIT AMOR PATRIAE" in Silver letters.

Symbolism
Blue and white are the colors used for Infantry, the original designation of the unit. The three battle honors awarded the organization for services during World War I are symbolized by the patriarchal cross, which represents Lorraine, where the regiment first entered combat in 1918; the oak tree which alludes to the woods of Meuse-Argonne, the general area of operations in France; and the lion, taken from the arms of Belgium, which represents the Ypres-Lys campaign in 1918. The motto translates to "Led by Love of Country."

History
The distinctive unit insignia was originally authorized for the 361st Infantry Regiment on 8 March 1927. It was redesignated for the 361st Regiment on 24 January 1962.

Source: The US Army Institute of Heraldry