We address the problem of the performance analysis of the Stochastic Fair Sharing (SFS) algorithm for fair link sharing. The SFS scheme has been proposed in [1] to carry out a fair link sharing and fair sharing among Virtual Private Networks (VPNs). Depending upon the current utilization and provisioned capacities of the classes, the SFS admission control algorithm decides which sessions to accept and which to reject. In this paper, we undertake the performance evaluation of the SFS scheme analytically. The main performance measure in our analysis is the session blocking probability. In particular, we obtain the Roberts-Kaufman's like recursion for the SFS scheme to compute the blocking probability. We then use linear programming techniques to compute the blocking probability from the above recursion.