He left the Conservatoire in Pardubice in 1985 as a graduate of professor Ivan Štraus. Then he studied at the Academy of Music Arts (AMU) in Prague in the class of professor Jiří Novák and visited chamber music classes of professor Antonín Kohout (both members of Smetana Quartet). During his studies at AMU he became the first violinist of the Wihan Quartet whose member he is still at present.
He took part in solo as well as quartet competitions. In 1981, he became the winner of the Kocian Violin Competition in Ústí nad Orlicí, Czech. In 1983, he won the second place in the Competition of Conservatoires in Ostrava, Czech. In 1985 he was the fifth at the Václav Huml Competition in Zagreb, Yugoslavia. In 1993, he was awarded honourable mention in Gorizia, Italy, and in 1994 he became laureate of the "Beethoven's Hradec" competition in Hradec nad Moravicí, Czech. He also took part in Music Master Classes of professor Ivan Bezrodny in Weimar, Germany. He frequently gives solo recitals as well as concerts with orchestra, both in our country and abroad (Zagreb Philharmonic, Košice Philharmonic, Pardubice Chamber Philharmonic, Virtuosi Pragensis, etc.). To celebrate 250th anniversary of J. S. Bach's death in 2000 he performed a series of concerts of all Bach's Sonatas and Partitas for violin solo at the Smeteana's Litomyšl festival in Czech.
As the first violinist of the Wihan Quartet he won the 1st prizes at the Prague Spring competition in 1988 and in London in 1991. In London, the ensemble also won the Prize of the Public. After that, the Wihan Quartet made many tours to European countries known for their tradition in chamber music as well as Singapore, Jordan, Australia, New Zealand, Japan, and the USA.
The Wihan Quartet made more than 20 CDs at various Czech recording companies. In 2005 it finished the complete set of Beethoven's quartets.
In 2002, Leoš Čepický made a Multisonic solo CD recording of Bach's Sonatas and Partitas.