Efficient ultrasonic noise reduction by using enclosures requires the knowledge of absorbing properties of materials in the frequency range above 4 kHz. However, standardized methods enable determination of absorption coefficients of materials in the frequency range up to 4 kHz. For this reason, it is proposed to carry out measurements of the sound absorption properties of materials in the free field by means of a tone-burst technique in the frequency range from 4 kHz to 40 kHz at angles of incidence varying from 0° to 60°. The absorption coefficient of a material is calculated from the reflection coefficient obtained by reflecting a tone-burst from both a perfectly reflecting panel and a combination of this panel and the sample of the tested material. The tests results show that mineral wool and polyurethane open-cell foam possess very good absorbing properties in this frequency range.