The elastic and magnetic properties of a single crystal of the bilayer manganese oxide ͑Pr 0.6 La 0.4 ͒ 1.2 Sr 1.8 Mn 2 O 7 have been investigated by means of ultrasonic and high-field magnetization measurements. Remarkable changes in the elastic constants C 11 , C 33 , C 44 , and C 66 as a function of temperature and magnetic field have been observed. In particular, a distinct elastic anomaly was observed at low temperatures and in magnetic fields when crossing the phase boundary between the paramagnetic insulating and the fieldinduced ferromagnetic metallic state. A pronounced elastic softening as a function of magnetic field ͑H͒ appears across the boundary of the low-temperature magnetic phase below around 40 K, accompanied by a distinct hysteresis. In the high-field region, however, these elastic constants exhibit a monotonic increase upon increasing the magnetic field. The high-field magnetization measurements characterizing the magnetic state point out a strong coupling between the elastic strain and the magnetic moment. The data can be described reasonably well considering a strong coupling between elastic strain and magnetic susceptibility m = ץM / ץH.