Buk graduated from Juliusz Słowacki high school in Kielce. In 1984 he graduated from the Academy of Armed Forces Officers in Poznań.
He served as commander of the Polish Land Forces until his death in the 2010 Polish Air Force Tu-154 crash near Smolensk. In 1984, he joined the 29th Medium Tank Regiment in Żagań and served in this unit until 1991. In 1991 he enrolled at the Faculty of Land Forces of the National Defence Academy in Warsaw.
Between 1993 and 1995 he served, inter alia, in the 18th Battalion Airborne assault and 6 Air Assault Brigade.
From 1995 to 1998, he served in the 25th Air Cavalry Brigade in Tomaszów Mazowiecki. In 1999, after completing the annual post-graduate command post in the United States of America, he was appointed deputy commander of his unit
From 2002 to 2005 he served as commander of the 34rd Armoured Cavalry Brigade in Zagan. In 2004 and 2005 he was deputy commander of Multinational Division Central-South in Iraq.
Between 2005 and 2006 he was deputy director of the North Atlantic Treaty Organization Joint Force Training Centre in Bydgoszcz.
On 15 June 2007, Buk was appointed commander of 1st Mechanised Division of Warsaw. On 25 July 2007, he took command of the IX amendment Nippon Electric Corporation and Multinational Division Center-South in Iraq On 15 September 2009 he was appointed by President Lech Kaczynski to commander of the Army. On 10 April 2010, he died in the presidential plane crash near Smolensk.
Military promotions.
Silver Medal in the Service of the Armed Forces of the Fatherland.