Shoulder Sleeve Insignia (SSI)
A Shoulder Sleeve Insignia (SSI) is a distinctive cloth patch worn on the left sleeve of a uniform just below the shoulder seam by individuals assigned to Army divisions, corps, and armies, to Air Force wings, and to other specifically authorized organizations and also worn on the right sleeve by individuals to indicate overseas service with certain units during periods of active operations. They are sometimes called or referred to as a shoulder patch.
There are two distinctive versions. There is the brightly colored version that often contain intricate designs with bright colors. While these are SSIs with their bright colors and designs are very beautiful to look at there is a risk standing out when a soldier is in combat or in hiding. Therefore the colored versions of the shoulder sleeve insignia in its color form were commonly only worn on the dress uniform or service uniform when a soldier was not in combat.
The second version, or subdued version, was originally created for the Battle Dress Uniform (BDU). These patches featured colored of primarily olive, dark brown and black, to match the BDU. HOWEVER, this version is relatively obsolete because the Army phased out the BDU in the late 2000s in favor of the Army Combat Uniform (ACU).
To this end there is the Desert Camouflage Uniform (DCU) and the SSI made a similar transition to primarily tan and "spice" brown, to match the uniform's design. Yet again the the Army phased out the DCU in favor of ACU. As of May 2020 the SSI are primarily foliage green, light brown, and black, though a few patches also feature red and maroon colors for some details.
With the development of the Operational Camouflage Pattern (OCP) uniform often referred to as MultiCam the SSI has yet again migrated to a new SSI which have the "Foliage" green of the ACU SSI being replaced by "Bagby" green.
Regardless, the SSI is a piece of art. They are designed by The Institute of Heraldry (TIOH). From the TIOH FAQs - A Shoulder Sleeve Insignia (SSI) and Distinctive Unit Insignia (DUI) are authorized for those units listed in AR 670-1. Units not listed in AR 670-1 (other than USAG) may request the authorization of insignia if the unit has at least 500 military assigned (250 for DA Operating Agencies). Army elements of a Combatant Command are authorized an SSI and DUI. For other organizations, a minimum of 500 military assigned is required to be authorized insignia.
These are the SSIs for the Armies, Groups, Corps, and Divisions
