Abstract After decades of service, concrete foundations may be in need of strengthening and retrofitting due to continuous aging. However, the main objective of this work is presenting a mathematical model for vibration of concrete foundation with nano fiber reinforced polymer (NFRP) layer resting on soil medium. The nano fibers of NFRP layer are made from carbon nanotubes (CNT) where the effective material properties of nano-composite structure are obtained by Mori-Tanaka model considering agglomeration effects. The soil medium is simulated with spring constants of Winker foundation model. Based on the sinusoidal shear deformation theory (SSDT), energy method and Hamilton's principle, the motion equations are derived. Applying Navier method, the frequency of the structure is calculated analytically so that the effects of volume percent and agglomeration of CNTs, soil medium, structural damping and geometrical parameters of structure are shown on the frequency of system. Results show that considering NFRP layer leads to higher frequency for NFRP thickness to concrete foundation thickness ratio of higher than 0.005.