This paper examines the efficient layout of VPs in an ATM network. The ATM network consists of ATM switches and their attached network end users, which may be gateways, routers, and hosts. The physical topology, the offered traffic, and call setup matrices of the network end users are assummed to be given. The problem is formulated as a flow-based optimization problem. A heuristic approach is presented which (i) establishes VPs according to physical network-specific and application-specific constraints and a cost function, (ii) provides multipaths between each source-destination user pair to minimize the call blocking probability and to increase network resilience, and (iii) uses a novel VP combining process which is guaranteed to always satisfy the switching constraints. Simulation results are presented for the proposed VP planning policy. Guidelines for the design of robust VP layouts and the efficient establishment of VCs are also presented.