Matvei Kapelyushnikov was born in a village of Abbas-Tumani in Akhaltsikhe uyezd in Tiflis guberniya. He began his career in the oil industry as a technical designer at an oil company called Baku Society of the Russian Oil in 1914. In 1915-1918, Matvei Kapelyushnikov was employed as a drilling rig designer and mechanical engineer at the Bykhovsky Refinery and then at a factory belonging to the Caspian Partnership oil company. In 1920-1924, he worked in the Azneft refineries administration in Baku. In 1920-1924, Matvei Kapelyushnikov was employed as a deputy head of the Azneft Technical Bureau. In 1933-1936, he held the director's post at the Azerbaijan Research Institute named after Valerian Kuybyshev. In 1937-1959, Kapelyushnikov headed the petroleum reservoir physics lab at the Oil Institute of the Soviet Academy of Sciences. He had been a drilling department professor at the Moscow Oil Institute named after Ivan Gubkin since 1945.
Matvei Kapelyushnikov's scientific work was dedicated to the extracting and refining technologies of oil and gas due to the intensified development of the petroleum industry during the years of the establishment of Soviet authority and especially post-World War II years. Kapelyushnikov's most famous invention was the revolutionary turbodrill - a hydraulic bottom-hole drill for drilling wells. It was patented in the United Kingdom (March 11, 1925) and then in the USSR (August 31, 1925).