  In this paper attention is focused on gravitational sector of the
Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for
gravitational field are derived. The asymptotic for modified Schwarzschild
solution is obtained, as a decomposition in parameter $L \approx 10^{-32}$ cm.
It is shown, that singularity at $r = 0$ is absent, being replaced by a `ball
of matter' with finite dimensions, such that density of matter is of order of
magnitude of the Planck's density. Another solution of the same symmetry is
obtained, corresponding to a closed space of finite volume of order $L^3$.
