In this paper the authors propose a method for designing the Virtual Private Network (VPN) that guarantees a strict Quality of Service (QoS) over IP networks. The assumed QoS metric is PLP (Packet Loss Probability), and it is guaranteed probabilistically by the provision of an appropriate equivalent bandwidth. We consider two network architectures for constructing VPN, the customer pipe scheme and the Hose scheme, and we present an analytic model to compute the amount of the required bandwidth for the two schemes. Finally, we investigate the validity of the proposition via numerical experiments.