Approximate expressions are discussed which are applicable for acoustic quantities in the vicinity of a plane piston source of ultrasound which radiates into an absorbing medium. A particularly useful approach for nearfield calculations combines an expression valid near the axis with another, given by Pierce [Acoustics,AnIntroductiontoItsPhysicalPrinciplesandApplications(McGraw‐Hill, New York, 1981), Chap. 5], which is valid elsewhere. This approach gives reasonable accuracy at relatively low computational cost. Computed plots are presented, showing spatial distributions of the square of the pressure amplitude. Most of the plots are for a source diameter of 1.2 cm, a frequency of 3 MHz, and an absorption coefficient of 0.15 Np/cm; these are representative of conditions for medical applications of ultrasound.