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• The influence of flexoelectricity, micro-stiffness and micro-inertia effects on the Rayleigh wave propagation is studied. • The micro-stiffness increases Rayleigh wave velocity, while the micro-inertia and flexoelectricity decrease its value. • The effect of material microstructure and flexoelectricity is important for short wavelengths. • The dispersion curve profile depends on the ratios between flexoelectric coefficients and material lengths scale parameters. A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials. [ABSTRACT FROM AUTHOR]