Major General Jelinsky graduated from the United States Military Academy in 1973 and was commissioned as a Second Lieutenant of Field Artillery in the Regular Army. His military schooling includes the Field Artillery Officer Basic Course, Supply Management Officer Course, Quartermaster Officer Advanced Course, Field Artillery Officer Advanced Course, Command and General Staff College, Reserve Component National Security Course and Army War College. He served in the Panama Canal Zone with Bravo Battery, 22nd Field Artillery. Later at Fort Devens, Massachusetts, he served as Battalion S-4 and as Commander of the 278th General Supply Company.
After leaving active duty, he commanded Headquarters and Headquarters Company, 137th Supply & Service Battalion in the Ohio Army National Guard. General Jelinsky transferred to the United States Army Reserves and assumed command of F Battery, 1/334th Regiment, 84th Division where he served until joining the 633rd Corps Support Group in Madison, Wisconsin. General Jelinsky was the S-4 Officer and in 1987 was reassigned as S-3 of the 633rd. His next assignment was Executive Officer, 213th Supply and Service Battalion, Wausau, Wisconsin. He was the Battalion S-2/3 and Support Operations Officer during the 213th activation for Operations Desert Shield/Storm in Saudi Arabia in 1990 and 1991. General Jelinsky commanded the 213th Supply & Service Battalion. In 1996 he was selected for Deputy Chief of Staff Force Development, 88th Regional Support Commander where he served until taking command of the 633rd Corps Support Group on 12 September 1997. On 10 February 2000, he was assigned as the Deputy Commanding General of the 88th Regional Support Command. His final assignment was Deputy Commander for Mobilization and Reserve Affairs of USSOUTHCOM.
His final assignment was as Deputy Commander for Mobilization and Reserve Affairs of United States Southern Command.

MG Jelinsky’s military decorations include the Defense Superior Service Medal, Legion of Merit, Bronze Star Medal, Meritorious Service Medal, Humanitarian Service Medal, Parachutist Badge and Scuba Divers Badge.