Using Monte Carlo simulation of the modem scenario of the evolution of binary systems (the '' Scenario Machine''), we calculated the number of binary radiopulsars with black holes and some their observational properties. The comparison with observations imposes some restrictions on the minimal mass of the star-progenitor collapsing to a black hole, M(cr), and the fraction of the mass that collapses to the black hole, k(bh) = M(bh)/M*, the probable values being M(cr) almost-equal-to 35 M. and k(bh) almost-equal-to 0.3. Our calculations show that binary radiopulsars on eccentric orbits around black holes must be discovered in the near future.