In order to solve the problem of the interference management in D2D(device-to-device) underlaid cellular networks, a new design of stochastic geometry based access control for D2D communications was proposed. Based on the stochastic process theory and the stochastic geometry tool, the cellular services′ access failure probability expression was derived to determine the impact from other-cell base stations and D2D communications on the cellular communication. Given the constraint of access failure probability, the maximum D2D transmitters density was calculated according to the expression. As a result, the base stations realized the access control for D2D users and guaranteed the access failure probability of cellular services. The calculated access failure probability of cellular services was validated by extensive simulations. The simulation results verify that the estimation result from the proposed numerical calculation is consistent with the Monte Carlo simulation result, and the cellular services′ access failure probability requirement can be satisfied by limiting the density and the transmission power of D2D transmitters.