Anastasia Kobekina was born in a family of musician in Yekaterinburg, Russia. She received her first cello lessons when she was 4 years old. She began her studies at her hometown, continuing later in the Central Music School in Moscow. From 2012 Anastasia is studying at Kronberg Academy Masters with Frans Helmerson, these studies are funded by the Steigenberger/Rath Stipendium.

In Russia, Anastasia was first-prize winner of several international competitions, such as the television contest "Nutcracker" in 2007 and the competition "New names" (2008); she was finalist of the international contest "Eurovision Young Musicians" in Vienna in 2008.

In 2015 Anastasia was a semi-finalist at Tchaikovsky Competition in Moscow and later in September 2015 she won the first prize at the TONALi Competition in Hamburg, Germany.

As a soloist Anastasia played with orchestras such as the Moscow Virtuosi, Kremerata Baltica,the Vienna Symphony Orchestra, the Sinfonia Varsovia, the National Russian Philharmonic and Mariinsky Theater Orchestra - under guidance of Krzysztov Penderecki, Heinrich Schiff, Vladimir Spivakov, Valery Gergiev and Peter Gülke.

She has been playing on many festivals, including“Rising stars in the Kremlin” (2010), Cello festival in Kronberg (2011, 2013, 2015), Festival in Annecy, Colmar and Mecklenburg-Vorpommern. In 2012 she participated in Chamber Music Connects the World performing with Gidon Kremer, Yuri Bashmet and Andras Schiff.

In 2019 Anastasia Kobekina won the 3rd prize at the Tchaikowsky Competition Moscow.

In 2012 Anastasia received Stipendium named after famous cellist Boris Pergamenschikov. Anastasia plays a cello by Giovanni Baptista Guadagnini, 1743.