  In this paper we describe a model of a four-dimensional spherically symmetric
black hole in a limiting curvature theory of gravity. In this theory the
Einstein-Hilbert action is modified by adding to the action terms providing
inequality constraints on chosen curvature invariants. We demonstrated that in
such a model, instead of formation of the curvature singularity, the spacetime
remains regular in the black hole interior. For black holes with gravitational
radius much larger than the radius $\ell$ of the critical curvature the
obtained solutions describe a space exponentially expanding in one direction
and periodically oscillating in the other two (spherical) directions.
