•Mechanical responses of a plate excited by laser pulses were effectively detected.•Thickness resonance frequency and time of arrival are independent parameters.•Reliefs of both plate surfaces were visualized together with the plate thickness.•One of the measured reliefs is unaffected by changes in the plate material. Local ultrasonic resonance spectroscopy (LURS) is a new approach to material inspection, where the specimen is locally excited by a short mechanical impulse while its local mechanical response is recorded at a position nearby. The local material and geometrical properties can be extracted from the frequency spectrum of the response and visualized by performing a scan over the inspected area. In our experiment, the plate thickness and the reliefs of both plate surfaces (plate curvature) were obtained from thickness resonance and time of arrival analysis without physical contact to the specimen. Ultrasound was generated on the specimen surface by a laser pulse. Local mechanical response of a carbon fiber-reinforced polymer plate with a thickness ranging from 0.6 mm to 4.3 mm was recorded with a broadband optical microphone in through-transmission setup. The precision of this arrangement greatly exceeded the precision of conventional methods limited by the ultrasound wavelength. For thicknesses in the range around 1 mm, standard deviations of up to several µm were achieved. An influence of the through-plate ultrasound velocity on the measured relief of the plate surface nearest to the optical microphone was eliminated by a joint evaluation of thickness resonance and time of arrival. Furthermore, we demonstrated that internal delaminations have an influence on the spectrum of the local mechanical response and can therefore be detected by LURS.