  We study the influence of fluctuations in molecular shape on the stability of
the biaxial nematic phase by generalizing the mean field model of Mulder and
Ruijgrok [Physica A {\bf 113}, 145 (1982)]. We limit ourselves to the case when
the molecular shape anisotropy, represented by the alignment tensor, is a
random variable of an annealed type. A prototype of such behavior can be found
in lyotropic systems - a mixture of potassium laurate, 1-decanol, and $D_2O$,
where distribution of the micellar shape adjusts to actual equilibrium
conditions. Further examples of materials with the biaxial nematic phase, where
molecular shape is subject to fluctuations, are thermotropic materials composed
of flexible trimeric- or tetrapod-like molecular units. Our calculations show
that the Gaussian equilibrium distribution of the variables describing
molecular shape (dispersion force) anisotropy gives rise to new classes of the
phase diagrams, absent in the original model. Depending on properties of the
shape fluctuations, the stability of the biaxial nematic phase can be either
enhanced or depressed, relative to the uniaxial nematic phases. In the former
case the splitting of the Landau point into two triple points with a direct
phase transition line from isotropic to biaxial phase is observed.
