Like many musicians, he inherited close relationship to music from his parents, mainly through singing in the car on the way to the family weekend cottage. Both his siblings, Zdeněk Zelba and Lenka Machová, also play in the Czech Philharmonic. He began playing the violin and later viola at local Music School but with the approaching conservatory entrance exams, he fell ill and was unable to practice. His father suggested switching to a wind instrument, such as oboe like the tall elegant Czech Philharmonic musician on TV. He then studied oboe at the Prague Conservatory with Pavel Verner, soloist of the Prague Symphony Orchestra and an excellent chamber musician, and Otto Trnka, first oboist of the National Theatre Orchestra. In 1985–1988, he taught at the local Music School in Modřany. In 1997, he graduated from the Academy of Performing Arts in Prague, having studied with Professor Jiří Mihule, the elegant man on TV, who had already been working with him in preparation for the conservatory entrance exams.
He first tasted chamber music while studying, he was a member of a wind quintet and later an octet. Thanks to these ensembles, he also had the chance to travel to the West (Germany and Sweden). His friends from the Army Artistic Ensemble, where he completed his compulsory military service, brought him back to string instruments. He played the viola in a cimbalom ensemble and even a string quartet. He was thinking about abandoning oboe altogether but succeeded in auditions to the Prague Symphony Orchestra FOK in 1988. Nevertheless, he decided to join the Czech Philharmonic instead as the second oboe player and later also cor anglais player. He has performed with various chamber ensembles, including hundreds of concerts with Musica Gaudeans Quartet, the band Camael, which is somewhere between folk, country and jazz, collaborating with violinist and composer Pavel Fischer and the Prague Baroque Soloists alongside his Czech Philharmonic colleagues. As a soloist, he has played with the Philharmonic Chamber Orchestra and Talich Chamber Orchestra. He has appeared as the guest principal oboist in the Czech National Symphony Orchestra and the South Czech Philharmonic. He has never forgotten folk music. Since 1982, he has been regularly playing with Chorea Bohemica ensemble where he met excellent composer, singer and musician Jaroslav Krček. He often plays and sings Czech, Moravian and Slovak folk songs with his brother Zdeněk.
He has recently been enjoying work with the Cimbalom Ensemble of the Czech Philharmonic the most. The group is specific for a number of reasons, mainly because they have oboe (alternating with cor anglais or recorders) instead of clarinet. They are also not limited to folk songs but perform Baroque music (only exchange the soft cimbalom sticks for hard ones and the sound is undistinguishable from a harpsichord), focusing on pieces inspired by folk music. Many famous composers based their work on folk music and the ensemble just decided to go the other way, playing Johannes Brahms, Béla Bartók, Zoltán Kodály, Franz Liszt, Bedřich Smetana and Leoš Janáček.