  In the present paper we generalised a phenomenological model developed in
\cite{gomo:2005} for the description of magnetostructural phase transitions and
related peculiarities of elastic properties in solid oxygen under high pressure
and/or low (below 40 K) temperature. We show that variation of all the lattice
parameters in the vicinity of $\alpha\beta$-phase transition is due to both the
shift of basal closed packed planes and appearance of the long-range magnetic
order. Competition between these two factors from one side and lattice
compression below $T_{\alpha\beta}$ from another produces non monotonic
temperature dependence of lattice parameter $b$ (along monoclinic axis). Steep
decrease of the sound velocities in the vicinity of $T_{\alpha\beta}$ can be
explained by the softening of the lattice with respect to shift of the
close-packed planes (described by the constant $K_2$) prior to phase transition
point. We anticipate an analogous softening of sound velocities in the vicinity
of $\alpha \delta$-phase transition and non monotonic pressure dependence of
sound velocities in $\alpha$-phase.
