As a further commitment to his homeland, Bashmet founded the International Foundation which bears his name in 1994.  It awards the 'Shostakovich Prize' each year - recipients have included Gidon Kremer, Anne-Sofie Mutter, Viktor Tretiakov, Valery Gergiev, Olga Borodina and Thomas Quastoff.  There are also modest stipends for young musicians as well as grants for retired musicians or dependants, such as the wife of  the 'grandfather of Russian viola', Vadim Borisovsky, who is nearly 100 years old.

The Yuri Bashmet Foundation is established as part of the Kronberg Academy - inspired by the Kronberg Academy's Violin Festival and Mstislav Rostropovich's Cello Foundation. With the help of this Foundation, the Kronberg Academy supports young violists taking part in the 'Chamber Music Connects the World' project. The activities of the Trust are complemented by Viola Foundation instruments, made available to scholarship winners. In addition, Yuri himself participates in the Academy's Chamber Music project, held every other year.