  The elastic and magnetic properties of a single crystal of 327 bilayer
manganese oxide $(La_{1-z} Pr_z)_{1.2} Sr_{1.8} Mn_2 O_7$ with $z$=0.6 have
been investigated by ultrasonic and high-field magnetization measurements. A
distinct elastic anomaly was observed at low temperatures and in high magnetic
fields when crossing the phase boundary. A pronounced elastic softening as a
function of magnetic field ($H$) 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
an increase with increasing a magnetic field in the high-field region. The
high-field magnetization measurement characterizing the magnetic state
clarified a strong connection between elastic strains and magnetic moments. The
new metamagnetic transition was found in the high-field region above 40 K,
accompanied with no hysteresis. The present results of elastic constants are
discussed in terms of a coupling effect between elastic strains associated with
sound waves and relevant magnetic moments, and relevant conduction bands. They
are explained reasonably in terms of a strong coupling between elastic strains
and magnetic susceptibility $chi$$_{m}$=$partial$$M$/$partial$$H$.
