The result of the research aims to provide a foundation structure that reduces the amplitude of oscillation of machines and equipment from various technical causes and natural phenomena, preventing resonant phenomena and economical use of foundation material. The proposed foundation, compared to existing foundations, provides a decrease in amplitude and prevents the phenomenon of resonance of vibrations of foundations for machines and equipment creating savings in the use of cement-concrete material. There is considered mathematical, structural, and practical modeling of anti-vibration foundations of mechanical installations in this article. The purpose of the study is to create a foundation design that reduces the amplitude of oscillation of structures from various technical reasons and natural phenomena, prevents resonant phenomena, and economical use of foundation-reinforced concrete material. The research results can be used in the design of foundations of piston machines and equipment used in the oil and gas industry.