Home‐built resonance ultrasound microscopy is presented for quantitatively determining local Young’s modulus and local internal friction of materials. It evaluates the elastic properties from resonance frequencies and attenuation of an isolated langasite oscillator, touching the examined material. Noncontacting measurement (wireless and electrodeless) of the resonance frequency and attenuation of the oscillator has been achieved with a line antenna by the piezoelectric effect. The oscillator is supported by a fixture exactly at nodal points, and it touches the material at an antinodal point. Thus, acoustical contact on the oscillator surfaces occurs only at one point with the material, providing high sensitivity to the modulus and damping in the local area. Formulation of relationships between material’s stiffness and internal friction, and oscillator’s resonance frequency and attenuation is proposed using the generalized Hertzian‐contact model. Results for polycrystalline copper, dual‐phase stainless steel, and NbTi/Cu superconducting wire are shown, giving important knowledge including stiffness distribution within a crystallite. The results are compared by electron‐backscattering‐pattern measurements.