  We discuss a recently proposed limiting curvature theory of gravity and its
application to the problem of singularities inside black holes. In this theory
the growth of the curvature is suppressed by specially chosen inequality
constraints included in the gravity action. We consider a case of a spherically
symmetric four dimensional black hole and demonstrated that imposed curvature
constraints modify a solution in the black hole interior. Instead of forming
the curvature singularity the modified metric describes a space which is
exponentially expanding in one direction and oscillating the other two
directions. The spacetime is complete and its polynomial curvature invariants
are uniformly bounded.
