Local ultrasonic resonance spectroscopy (LURS) is a new approach to ultrasound signal analysis, which was necessitated by a novel inspection method capable of the contact-free, localized, broadband generation and detection of ultrasound. By performing a LURS scan, it is possible to detect local mechanical resonances of various features and of the specimen itself. They are highly sensitive to local mechanical properties. By observing different parameters in the frequency spectrum (e.g., resonance amplitude and resonance peak frequency), geometrical, material and condition properties can be visualized for all of the scanning positions. We demonstrate LURS for inspection of a carbon fiber reinforced polymer plate. Local defect resonances of delaminations and a flat-bottom hole were detected in the frequency range from 25 to 110 kHz. Analyzing the higher frequency range (0.3 MHz to 1.5 MHz) of the same scan, the shift of the thickness resonance frequency of the plate and its higher-order resonance frequencies carry the information about the aluminum inclusions. LURS shows an advantage in characterizing the localized features of the specimens via contact-free ultrasonic inspection.